Digraphs: theory, algorithms and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
2006
|
| Ausgabe: | 2. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 683 - 715 |
| Beschreibung: | XXII, 754 S. graph. Darst. |
| ISBN: | 1852336110 9781852336110 |
Internformat
MARC
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| 020 | |a 9781852336110 |9 978-1-85233-611-0 | ||
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| 100 | 1 | |a Bang-Jensen, Jørgen |d 1960- |e Verfasser |0 (DE-588)142714992 |4 aut | |
| 245 | 1 | 0 | |a Digraphs |b theory, algorithms and applications |c Jørgen Bang-Jensen and Gregory Gutin |
| 250 | |a 2. print. | ||
| 264 | 1 | |a London |b Springer |c 2006 | |
| 300 | |a XXII, 754 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 683 - 715 | ||
| 650 | 4 | |a Gerichteter Graph | |
| 650 | 4 | |a Directed graphs | |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gerichteter Graph |0 (DE-588)4156815-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Digraph |0 (DE-588)4012307-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexitätstheorie |0 (DE-588)4120591-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gerichteter Graph |0 (DE-588)4156815-1 |D s |
| 689 | 0 | 1 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | 2 | |a Komplexitätstheorie |0 (DE-588)4120591-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Digraph |0 (DE-588)4012307-8 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Gutin, Gregory Z. |d 1957- |e Verfasser |0 (DE-588)142715557 |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016156075&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016156075 | |
Datensatz im Suchindex
| _version_ | 1808045746099847168 |
|---|---|
| adam_text |
CONTENTS
1.
BASIC
TERMINOLOGY,
NOTATION
AND
RESULTS
.
1
1.1
SETS,
SUBSETS,
MATRICES
AND
VECTORS
.
1
1.2
DIGRAPHS,
SUBDIGRAPHS,
NEIGHBOURS,
DEGREES
.
2
1.3
ISOMORPHISM
AND
BASIC
OPERATIONS
ON
DIGRAPHS
.
6
1.4
WALKS,
TRAILS,
PATHS,
CYCLES
AND
PATH-CYCLE
SUBDIGRAPHS
.
10
1.5
STRONG
AND
UNILATERAL
CONNECTIVITY
.
16
1.6
UNDIRECTED
GRAPHS,
BIORIENTATIONS
AND
ORIENTATIONS
.
18
1.7
MIXED
GRAPHS
AND
HYPERGRAPHS
.
22
1.8
CLASSES
OF
DIRECTED
AND
UNDIRECTED
GRAPHS
.
25
1.9
ALGORITHMIC
ASPECTS
.
28
1.9.1
ALGORITHMS
AND
THEIR
COMPLEXITY
.
29
1.9.2
A/"P-COMPLETE
AND
.VP-HARD
PROBLEMS
.
33
1.10
APPLICATION:
SOLVING
THE
2-SATISFIABILITY
PROBLEM
.
35
1.11
EXERCISES
.
38
2.
DISTANCES
.
45
2.1
TERMINOLOGY
AND
NOTATION
ON
DISTANCES
.
46
2.2
STRUCTURE
OF
SHORTEST
PATHS
.
48
2.3
ALGORITHMS
FOR
FINDING
DISTANCES
IN
DIGRAPHS
.
50
2.3.1
BREADTH-FIRST
SEARCH
(BFS)
.
50
2.3.2
ACYCLIC
DIGRAPHS
.
52
2.3.3
DIJKSTRA
'
S
ALGORITHM
.
53
2.3.4
THE
BELLMAN-FORD-MOORE
ALGORITHM
.
55
2.3.5
THE
FLOYD-WARSHALL
ALGORITHM
.
58
2.4
INEQUALITIES
BETWEEN
RADIUS,
OUT-RADIUS
AND
DIAMETER
.
59
2.4.1
RADIUS
AND
DIAMETER
OF
A
STRONG
DIGRAPH
.
59
2.4.2
EXTREME
VALUES
OF
OUT-RADIUS
AND
DIAMETER
.
60
2.5
MAXIMUM
FINITE
DIAMETER
OF
ORIENTATIONS
.
61
2.6
MINIMUM
DIAMETER
OF
ORIENTATIONS
OF
MULTIGRAPHS
.
63
2.7
MINIMUM
DIAMETER
ORIENTATIONS
OF
COMPLETE
MULTIPARTITE
GRAPHS
.
67
2.8
MINIMUM
DIAMETER
ORIENTATIONS
OF
EXTENSIONS
OF
GRAPHS
.
69
2.9
MINIMUM
DIAMETER
ORIENTATIONS
OF
CARTESIAN
PRODUCTS
OF
GRAPHS
.
71
XVI
CONTENTS
2.10
KINGS
IN
DIGRAPHS
.
74
2.10.1
2-KINGS
IN
TOURNAMENTS
.
74
2.10.2
KINGS
IN
SEMICOMPLETE
MULTIPARTITE
DIGRAPHS
.
75
2.10.3
KINGS
IN
GENERALIZATIONS
OF
TOURNAMENTS
.
78
2.11
APPLICATION:
THE
ONE-WAY
STREET
AND
THE
GOSSIP
PROBLEMS
.
78
2.11.1
THE
ONE-WAY
STREET
PROBLEM
AND
ORIENTATIONS
OF
DI
GRAPHS
.
79
2.11.2
THE
GOSSIP
PROBLEM
.
80
2.12
APPLICATION:
EXPONENTIAL
NEIGHBOURHOOD
LOCAL
SEARCH
FOR
THE
TSP
.
82
2.12.1
LOCAL
SEARCH
FOR
THE
TSP
.
82
2.12.2
LINEAR
TIME
SEARCHABLE
EXPONENTIAL
NEIGHBOURHOODS
FOR
THE
TSP
.
84
2.12.3
THE
ASSIGNMENT
NEIGHBOURHOODS
.
85
2.12.4
DIAMETERS
OF
NEIGHBOURHOOD
STRUCTURE
DIGRAPHS
FOR
THE
TSP
.
86
2.13
EXERCISES
.
89
3.
FLOWS
IN
NETWORKS
.
95
3.1
DEFINITIONS
AND
BASIC
PROPERTIES
.
95
3.1.1
FLOWS
AND
THEIR
BALANCE
VECTORS
.
96
3.1.2
THE
RESIDUAL
NETWORK
.
98
3.2
REDUCTIONS
AMONG
DIFFERENT
FLOW
MODELS
.
99
3.2.1
ELIMINATING
LOWER
BOUNDS
.
99
3.2.2
FLOWS
WITH
ONE
SOURCE
AND
ONE
SINK
.
100
3.2.3
CIRCULATIONS
.
101
3.2.4
NETWORKS
WITH
BOUNDS
AND
COSTS
ON
THE
VERTICES
.
102
3.3
FLOW
DECOMPOSITIONS
.
104
3.4
WORKING
WITH
THE
RESIDUAL
NETWORK
.
105
3.5
THE
MAXIMUM
FLOW
PROBLEM
.
108
3.5.1
THE
FORD-FULKERSON
ALGORITHM
.
110
3.5.2
MAXIMUM
FLOWS
AND
LINEAR
PROGRAMMING
.
113
3.6
POLYNOMIAL
ALGORITHMS
FOR
FINDING
A
MAXIMUM
(S,T)-FLOW
.
114
3.6.1
FLOW
AUGMENTATIONS
ALONG
SHORTEST
AUGMENTING
PATHSLL4
3.6.2
BLOCKING
FLOWS
IN
LAYERED
NETWORKS
AND
DINIC
'
S
AL
GORITHM
116
3.6.3
THE
PREFLOW-PUSH
ALGORITHM
.
117
3.7
UNIT
CAPACITY
NETWORKS
AND
SIMPLE
NETWORKS
.
122
3.7.1
UNIT
CAPACITY
NETWORKS
.
122
3.7.2
SIMPLE
NETWORKS
.
124
3.8
CIRCULATIONS
AND
FEASIBLE
FLOWS
.
125
3.9
MINIMUM
VALUE
FEASIBLE
(S,
T)-FLOWS
.
127
3.10
MINIMUM
COST
FLOWS
.
128
3.10.1
CHARACTERIZING
MINIMUM
COST
FLOWS
.
131
3.10.2
BUILDING
UP
AN
OPTIMAL
SOLUTION
.
134
CONTENTS
XVII
3.11
APPLICATIONS
OF
FLOWS
.
137
3.11.1
MAXIMUM
MATCHINGS
IN
BIPARTITE
GRAPHS
.
137
3.11.2
THE
DIRECTED
CHINESE
POSTMAN
PROBLEM
.
141
3.11.3
FINDING
SUBDIGRAPHS
WITH
PRESCRIBED
DEGREES
.
142
3.11.4
PATH-CYCLE
FACTORS
IN
DIRECTED
MULTIGRAPHS
.
143
3.11.5
CYCLE
SUBDIGRAPHS
COVERING
SPECIFIED
VERTICES
.
145
3.12
THE
ASSIGNMENT
PROBLEM
AND
THE
TRANSPORTATION
PROBLEM.
.
147
3.13
EXERCISES
.
158
4.
CLASSES
OF
DIGRAPHS
.
171
4.1
DEPTH-FIRST
SEARCH
.
172
4.2
ACYCLIC
ORDERINGS
OF
THE
VERTICES
IN
ACYCLIC
DIGRAPHS
.
175
4.3
TRANSITIVE
DIGRAPHS,
TRANSITIVE
CLOSURES
AND
REDUCTIONS
.
176
4.4
STRONG
DIGRAPHS
.
179
4.5
LINE
DIGRAPHS
.
182
4.6
THE
DE
BRUIJN
AND
KAUTZ
DIGRAPHS
AND
THEIR
GENERALIZATIONS
187
4.7
SERIES-PARALLEL
DIGRAPHS
.
191
4.8
QUASI-TRANSITIVE
DIGRAPHS
.
195
4.9
THE
PATH-MERGING
PROPERTY
AND
PATH-MERGEABLE
DIGRAPHS
.
198
4.10
LOCALLY
IN-SEMICOMPLETE
AND
LOCALLY
OUT-SEMICOMPLETE
DI
GRAPHS
.
200
4.11
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
202
4.11.1
ROUND
DIGRAPHS
.
203
4.11.2
NON-STRONG
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
207
4.11.3
STRONG
ROUND
DECOMPOSABLE
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
209
4.11.4
CLASSIFICATION
OF
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
211
4.12
TOTALLY
^-DECOMPOSABLE
DIGRAPHS
.
215
4.13
INTERSECTION
DIGRAPHS
.
217
4.14
PLANAR
DIGRAPHS
.
219
4.15
APPLICATION:
GAUSSIAN
ELIMINATION
.
221
4.16
EXERCISES
.
224
5.
HAMILTONICITY
AND
RELATED
PROBLEMS
.
227
5.1
NECESSARY
CONDITIONS
FOR
HAMILTONICITY
OF
DIGRAPHS
.
229
5.1.1
PATH-CONTRACTION
.
229
5.1.2
QUASI-HAMILTONICITY
.
230
5.1.3
PSEUDO-HAMILTONICITY
AND
1-QUASI-HAMILTONICITY
.
232
5.1.4
ALGORITHMS
FOR
PSEUDO
AND
QUASI-HAMILTONICITY
.
233
5.2
PATH
COVERING
NUMBER
.
234
5.3
PATH
FACTORS
OF
ACYCLIC
DIGRAPHS
WITH
APPLICATIONS
.
235
5.4
HAMILTON
PATHS
AND
CYCLES
IN
PATH-MERGEABLE
DIGRAPHS
.
237
5.5
HAMILTON
PATHS
AND
CYCLES
IN
LOCALLY
IN-SEMICOMPLETE
DI
GRAPHS
.
238
5.6
HAMILTON
CYCLES
AND
PATHS
IN
DEGREE-CONSTRAINED
DIGRAPHS
.
240
XVIII
CONTENTS
5.6.1
SUFFICIENT
CONDITIONS
.
240
5.6.2
THE
MULTI-INSERTION
TECHNIQUE
.
246
5.6.3
PROOFS
OF
THEOREMS
5.6.1
AND
5.6.5
.
248
5.7
LONGEST
PATHS
AND
CYCLES
IN
SEMICOMPLETE
MULTIPARTITE
DI
GRAPHS
.
250
5.7.1
BASIC
RESULTS
.
251
5.7.2
THE
GOOD
CYCLE
FACTOR
THEOREM
.
253
5.7.3
CONSEQUENCES
OF
LEMMA
5.7.12
.
256
5.7.4
YEO
'
S
IRREDUCIBLE
CYCLE
SUBDIGRAPH
THEOREM
AND
ITS
APPLICATIONS
.
259
5.8
LONGEST
PATHS
AND
CYCLES
IN
EXTENDED
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
264
5.9
HAMILTON
PATHS
AND
CYCLES
IN
QUASI-TRANSITIVE
DIGRAPHS
.
265
5.10
VERTEX-HEAVIEST
PATHS
AND
CYCLES
IN
QUASI-TRANSITIVE
DIGRAPHS269
5.11
HAMILTON
PATHS
AND
CYCLES
IN
VARIOUS
CLASSES
OF
DIGRAPHS
.
273
5.12
EXERCISES
.
276
6.
HAMILTONIAN
REFINEMENTS
.
281
6.1
HAMILTONIAN
PATHS
WITH
A
PRESCRIBED
END-VERTEX
.
282
6.2
WEAKLY
HAMILTONIAN-CONNECTED
DIGRAPHS
.
284
6.2.1
RESULTS
FOR
EXTENDED
TOURNAMENTS
.
284
6.2.2
RESULTS
FOR
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
289
6.3
HAMILTONIAN-CONNECTED
DIGRAPHS
.
292
6.4
FINDING
A
HAMILTONIAN
(Z,Y)-PATH
IN
A
SEMICOMPLETE
DIGRAPH
295
6.5
PANCYCLICITY
OF
DIGRAPHS
.
299
6.5.1
(VERTEX-)PANCYCLICITY
IN
DEGREE-CONSTRAINED
DIGRAPHS
.
299
6.5.2
PANCYCLICITY
IN
EXTENDED
SEMICOMPLETE
AND
QUASI
TRANSITIVE
DIGRAPHS
.
300
6.5.3
PANCYCLIC
AND
VERTEX-PANCYCLIC
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
303
6.5.4
FURTHER
PANCYCLICITY
RESULTS
.
306
6.5.5
CYCLE
EXTENDABILITY
IN
DIGRAPHS
.
308
6.6
ARC-PANCYCLICITY
.
309
6.7
HAMILTONIAN
CYCLES
CONTAINING
OR
AVOIDING
PRESCRIBED
ARCS
.
312
6.7.1
HAMILTONIAN
CYCLES
CONTAINING
PRESCRIBED
ARCS
.
312
6.7.2
AVOIDING
PRESCRIBED
ARCS
WITH
A
HAMILTONIAN
CYCLE
.
315
6.7.3
HAMILTONIAN
CYCLES
AVOIDING
ARCS
IN
2-CYCLES
.
317
6.8
ARC-DISJOINT
HAMILTONIAN
PATHS
AND
CYCLES
.
318
6.9
ORIENTED
HAMILTONIAN
PATHS
AND
CYCLES
.
321
6.10
COVERING
ALL
VERTICES
OF
A
DIGRAPH
BY
FEW
CYCLES
.
326
6.10.1
CYCLE
FACTORS
WITH
A
FIXED
NUMBER
OF
CYCLES
.
326
6.10.2
THE
EFFECT
OF
A(D)
ON
SPANNING
CONFIGURATIONS
OF
PATHS
AND
CYCLES
.
329
6.11
MINIMUM
STRONG
SPANNING
SUBDIGRAPHS
.
331
6.11.1
A
LOWER
BOUND
FOR
GENERAL
DIGRAPHS
.
331
CONTENTS
XIX
I
6.11.2
THE
MSSS
PROBLEM
FOR
EXTENDED
SEMICOMPLETE
DI
GRAPHS
.
332
6.11.3
THE
MSSS
PROBLEM
FOR
QUASI-TRANSITIVE
DIGRAPHS
.
334
6.11.4
THE
MSSS
PROBLEM
FOR
DECOMPOSABLE
DIGRAPHS
.
335
6.12
APPLICATION:
DOMINATION
NUMBER
OF
TSP
HEURISTICS
.
337
6.13
EXERCISES
.
339
7.
GLOBAL
CONNECTIVITY
.
345
7.1
ADDITIONAL
NOTATION
AND
PRELIMINARIES
.
346
7.1.1
THE
NETWORK
REPRESENTATION
OF
A
DIRECTED
MULTIGRAPH
348
7.2
EAR
DECOMPOSITIONS
.
349
7.3
MENGER
'
S
THEOREM
.
353
7.4
APPLICATION:
DETERMINING
ARC
AND
VERTEX-STRONG
CONNECTIVITY
355
7.5
THE
SPLITTING
OFF
OPERATION
.
358
7.6
INCREASING
THE
ARC-STRONG
CONNECTIVITY
OPTIMALLY
.
362
7.7
INCREASING
THE
VERTEX-STRONG
CONNECTIVITY
OPTIMALLY
.
367
7.7.1
ONE-WAY
PAIRS
.
368
7.7.2
OPTIMAL
FC-STRONG
AUGMENTATION
.
370
7.7.3
SPECIAL
CLASSES
OF
DIGRAPHS
.
371
7.7.4
SPLITTINGS
PRESERVING
A:-STRONG
CONNECTIVITY
.
373
7.8
A
GENERALIZATION
OF
ARC-STRONG
CONNECTIVITY
.
376
7.9
ARC
REVERSALS
AND
VERTEX-STRONG
CONNECTIVITY
.
378
7.10
MINIMALLY
FC-(ARC)-STRONG
DIRECTED
MULTIGRAPHS
.
381
7.10.1
MINIMALLY
FC-ARC-STRONG
DIRECTED
MULTIGRAPHS
.
382
7.10.2
MINIMALLY
FC-STRONG
DIGRAPHS
.
387
7.11
CRITICALLY
FC-STRONG
DIGRAPHS
.
391
7.12
ARC-STRONG
CONNECTIVITY
AND
MINIMUM
DEGREE
.
392
7.13
CONNECTIVITY
PROPERTIES
OF
SPECIAL
CLASSES
OF
DIGRAPHS
.
393
7.14
HIGHLY
CONNECTED
ORIENTATIONS
OF
DIGRAPHS
.
395
7.15
PACKING
CUTS
.
400
7.16
APPLICATION:
SMALL
CERTIFICATES
FOR
A:-(ARC)-STRONG
CONNECTIVITY
404
7.16.1
FINDING
SMALL
CERTIFICATES
FOR
STRONG
CONNECTIVITY
.
405
7.16.2
FINDING
FC-STRONG
CERTIFICATES
FOR
K
1
.
406
7.16.3
CERTIFICATES
FOR
A:-ARC-STRONG
CONNECTIVITY
.
408
7.17
EXERCISES
.
409
8.
ORIENTATIONS
OF
GRAPHS
.
415
8.1
UNDERLYING
GRAPHS
OF
VARIOUS
CLASSES
OF
DIGRAPHS
.
415
8.1.1
UNDERLYING
GRAPHS
OF
TRANSITIVE
AND
QUASI-TRANSITIVE
DIGRAPHS
.
416
8.1.2
UNDERLYING
GRAPHS
OF
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
419
8.1.3
LOCAL
TOURNAMENT
ORIENTATIONS
OF
PROPER
CIRCULAR
ARC
GRAPHS
.
421
8.1.4
UNDERLYING
GRAPHS
OF
LOCALLY
IN-SEMICOMPLETE DIGRAPHS424
8.2
FAST
RECOGNITION
OF
LOCALLY
SEMICOMPLETE
DIGRAPHS
.
429
XX
CONTENTS
I
8.3
ORIENTATIONS
WITH
NO
EVEN
CYCLES
.
432
8.4
COLOURINGS
AND
ORIENTATIONS
OF
GRAPHS
.
435
8.5
ORIENTATIONS
AND
NOWHERE
ZERO
INTEGER
FLOWS
.
437
8.6
ORIENTATIONS
ACHIEVING
HIGH
ARC-STRONG
CONNECTIVITY
.
443
8.7
ORIENTATIONS
RESPECTING
DEGREE
CONSTRAINTS
.
446
8.7.1
ORIENTATIONS
WITH
PRESCRIBED
DEGREE
SEQUENCES
.
446
8.7.2
RESTRICTIONS
ON
SUBSETS
OF
VERTICES
.
450
8.8
SUBMODULAR
FLOWS
.
451
8.8.1
SUBMODULAR
FLOW
MODELS
.
452
8.8.2
EXISTENCE
OF
FEASIBLE
SUBMODULAR
FLOWS
.
453
8.8.3
MINIMUM
COST
SUBMODULAR
FLOWS
.
457
8.8.4
APPLICATIONS
OF
SUBMODULAR
FLOWS
.
458
8.9
ORIENTATIONS
OF
MIXED
GRAPHS
.
462
8.10
EXERCISES
.
467
9.
DISJOINT
PATHS
AND
TREES
.
475
9.1
ADDITIONAL
DEFINITIONS
.
476
9.2
DISJOINT
PATH
PROBLEMS
.
477
9.2.1
THE
COMPLEXITY
OF
THE
FC-PATH
PROBLEM
.
478
9.2.2
SUFFICIENT
CONDITIONS
FOR
A
DIGRAPH
TO
BE
A;-LINKED
.
482
9.2.3
THE
A:-PATH
PROBLEM
FOR
ACYCLIC
DIGRAPHS
.
484
9.3
LINKINGS
IN
TOURNAMENTS
AND
GENERALIZATIONS
OF
TOURNAMENTS
487
9.3.1
SUFFICIENT
CONDITIONS
IN
TERMS
OF
(LOCAL-)CONNECTIVITY
488
9.3.2
THE
2-PATH
PROBLEM
FOR
SEMICOMPLETE
DIGRAPHS
.
492
9.3.3
THE
2-PATH
PROBLEM
FOR
GENERALIZATIONS
OF
TOURNAMENTS493
9.4
LINKINGS
IN
PLANAR
DIGRAPHS
.
497
9.5
ARC-DISJOINT
BRANCHINGS
.
500
9.5.1
IMPLICATIONS
OF
EDMONDS
'
BRANCHING
THEOREM
.
503
9.6
EDGE-DISJOINT
MIXED
BRANCHINGS
.
506
9.7
ARC-DISJOINT
PATH
PROBLEMS
.
507
9.7.1
ARC-DISJOINT
PATHS
IN
ACYCLIC
DIRECTED
MULTIGRAPHS
.
510
9.7.2
ARC-DISJOINT
PATHS
IN
EULERIAN
DIRECTED
MULTIGRAPHS
.
511
9.7.3
ARC-DISJOINT
PATHS
IN
TOURNAMENTS
AND
GENERALIZA
TIONS
OF
TOURNAMENTS
.
517
9.8
INTEGER
MULTICOMMODITY
FLOWS
.
520
9.9
ARC-DISJOINT
IN
AND
OUT-BRANCHINGS
.
522
9.10
MINIMUM
COST
BRANCHINGS
.
527
9.10.1
MATROID
INTERSECTION
FORMULATION
.
527
9.10.2
AN
ALGORITHM
FOR
A
GENERALIZATION
OF
THE
MIN
COST
BRANCHING
PROBLEM
.
528
9.10.3
THE
MINIMUM
COVERING
ARBORESCENCE
PROBLEM
.
535
9.11
INCREASING
ROOTED
ARC-STRONG
CONNECTIVITY
BY
ADDING
NEW
ARCS
.
536
9.12
EXERCISES
.
538
CONTENTS
XXI
10.
CYCLE
STRUCTURE
OF
DIGRAPHS
.
545
10.1
VECTOR
SPACES
OF
DIGRAPHS
.
546
10.2
POLYNOMIAL
ALGORITHMS
FOR
PATHS
AND
CYCLES
.
549
10.3
DISJOINT
CYCLES
AND
FEEDBACK
SETS
.
553
10.3.1
COMPLEXITY
OF
THE
DISJOINT
CYCLE
AND
FEEDBACK
SET
PROBLEMS
.
553
10.3.2
DISJOINT
CYCLES
IN
DIGRAPHS
WITH
MINIMUM
OUT-DEGREE
AT
LEAST
K
.
554
10.3.3
FEEDBACK
SETS
AND
LINEAR
ORDERINGS
IN
DIGRAPHS
.
557
10.4
DISJOINT
CYCLES
VERSUS
FEEDBACK
SETS
.
561
10.4.1
RELATIONS
BETWEEN
PARAMETERS
VI
AND
TI
.
561
10.4.2
SOLUTION
OF
YOUNGER
'
S
CONJECTURE
.
563
10.5
APPLICATION:
THE
PERIOD
OF
MARKOV
CHAINS
.
565
10.6
CYCLES
OF
LENGTH
K
MODULO
P
.
567
10.6.1
COMPLEXITY
OF
THE
EXISTENCE
OF
CYCLES
OF
LENGTH
K
MODULO
P
PROBLEMS
.
568
10.6.2
SUFFICIENT
CONDITIONS
FOR
THE
EXISTENCE
OF
CYCLES
OF
LENGTH
K
MODULO
P
.
570
10.7
'
SHORT
'
CYCLES
IN
SEMICOMPLETE
MULTIPARTITE
DIGRAPHS
.
573
10.8
CYCLES
VERSUS
PATHS
IN
SEMICOMPLETE
MULTIPARTITE
DIGRAPHS
.
577
10.9
GIRTH
.
580
10.10
ADDITIONAL
TOPICS
ON
CYCLES
.
583
10.10.1
CHORDS
OF
CYCLES
.
583
10.10.2
ADAM
'
S
CONJECTURE
.
584
LO.HEXERCISES
.
586
11.
GENERALIZATIONS
OF
DIGRAPHS
.
591
11.1
PROPERLY
COLOURED
TRAILS
IN
EDGE-COLOURED
MULTIGRAPHS
.
592
11.1.1
PROPERLY
COLOURED
EULER
TRAILS
.
594
11.1.2
PROPERLY
COLOURED
CYCLES
.
597
11.1.3
CONNECTIVITY
OF
EDGE-COLOURED
MULTIGRAPHS
.
601
11.1.4
ALTERNATING
CYCLES
IN
2-EDGE-COLOURED
BIPARTITE
MULTI
GRAPHS
.
604
11.1.5
LONGEST
ALTERNATING
PATHS
AND
CYCLES
IN
2-EDGE-COLOURED
COMPLETE
MULTIGRAPHS
.
607
11.1.6
PROPERLY
COLOURED
HAMILTONIAN
PATHS
IN
C-EDGE-COLOURED
COMPLETE
GRAPHS,
C
3
.
613
11.1.7
PROPERLY
COLOURED
HAMILTONIAN
CYCLES
IN
C-EDGE-COLOURED
COMPLETE
GRAPHS,
C
3
.
615
11.2
ARC-COLOURED
DIRECTED
MULTIGRAPHS
.
620
11.2.1
COMPLEXITY
OF
THE
ALTERNATING
DIRECTED
CYCLE
PROBLEM
621
11.2.2
THE
FUNCTIONS
/(N)
AND
G(N)
.
624
11.2.3
WEAKLY
EULERIAN
ARC-COLOURED
DIRECTED
MULTIGRAPHS.
.
626
11.3
HYPERTOURNAMENTS
.
627
11.3.1
OUT-DEGREE
SEQUENCES
OF
HYPERTOURNAMENTS
.
628
XXII
CONTENTS
11.3.2
HAMILTON
PATHS
.
629
11.3.3
HAMILTON
CYCLES
.
630
11.4
APPLICATION:
ALTERNATING
HAMILTON
CYCLES
IN
GENETICS
.
632
11.4.1
PROOF
OF
THEOREM
11.4.1
.
634
11.4.2
PROOF
OF
THEOREM
11.4.2
.
635
11.5
EXERCISES
.
636
12.
ADDITIONAL
TOPICS
.
639
12.1
SEYMOUR
'
S
SECOND
NEIGHBOURHOOD
CONJECTURE
.
639
12.2
ORDERING
THE
VERTICES
OF
A
DIGRAPH
OF
PAIRED
COMPARISONS
.
642
12.2.1
PAIRED
COMPARISON
DIGRAPHS
.
642
12.2.2
THE
KANO-SAKAMOTO
METHODS
OF
ORDERING
.
645
12.2.3
ORDERINGS
FOR
SEMICOMPLETE
PCDS
.
645
12.2.4
THE
MUTUAL
ORDERINGS
.
646
12.2.5
COMPLEXITY
AND
ALGORITHMS
FOR
FORWARD
AND
BACK
WARD
ORDERINGS
.
647
12.3
(FC,/)-KERNELS
.
650
12.3.1
KERNELS
.
650
12.3.2
QUASI-KERNELS
.
653
12.4
LIST
EDGE-COLOURINGS
OF
COMPLETE
BIPARTITE
GRAPHS
.
654
12.5
HOMOMORPHISMS
-
A
GENERALIZATION
OF
COLOURINGS
.
658
12.6
OTHER
MEASURES
OF
INDEPENDENCE
IN
DIGRAPHS
.
664
12.7
MATROIDS
.
665
12.7.1
THE
DUAL
OF
A
MATROID
.
667
12.7.2
THE
GREEDY
ALGORITHM
FOR
MATROIDS
.
668
12.7.3
INDEPENDENCE
ORACLES
.
669
12.7.4
UNION
OF
MATROIDS
.
670
12.7.5
TWO
MATROID
INTERSECTION
.
671
12.7.6
INTERSECTIONS
OF
THREE
OR
MORE
MATROIDS
.
672
12.8
FINDING
GOOD
SOLUTIONS
TO
VP-HARD
PROBLEMS
.
673
12.9
EXERCISES
.
677
REFERENCES
.
683
SYMBOL
INDEX
.
717
AUTHOR
INDEX
.
723
SUBJECT
INDEX
.
731 |
| adam_txt | |
| any_adam_object | 1 |
| any_adam_object_boolean | |
| author | Bang-Jensen, Jørgen 1960- Gutin, Gregory Z. 1957- |
| author_GND | (DE-588)142714992 (DE-588)142715557 |
| author_facet | Bang-Jensen, Jørgen 1960- Gutin, Gregory Z. 1957- |
| author_role | aut aut |
| author_sort | Bang-Jensen, Jørgen 1960- |
| author_variant | j b j jbj g z g gz gzg |
| building | Verbundindex |
| bvnumber | BV022951611 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.15 |
| callnumber-search | QA166.15 |
| callnumber-sort | QA 3166.15 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 ST 130 |
| ctrlnum | (OCoLC)255118023 (DE-599)BVBBV022951611 |
| dewey-full | 511.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| edition | 2. print. |
| format | Book |
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| id | DE-604.BV022951611 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:02:31Z |
| indexdate | 2024-08-22T00:33:08Z |
| institution | BVB |
| isbn | 1852336110 9781852336110 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016156075 |
| oclc_num | 255118023 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM |
| owner_facet | DE-19 DE-BY-UBM |
| physical | XXII, 754 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| spelling | Bang-Jensen, Jørgen 1960- Verfasser (DE-588)142714992 aut Digraphs theory, algorithms and applications Jørgen Bang-Jensen and Gregory Gutin 2. print. London Springer 2006 XXII, 754 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 683 - 715 Gerichteter Graph Directed graphs Graphentheorie (DE-588)4113782-6 gnd rswk-swf Gerichteter Graph (DE-588)4156815-1 gnd rswk-swf Digraph (DE-588)4012307-8 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Gerichteter Graph (DE-588)4156815-1 s Graphentheorie (DE-588)4113782-6 s Komplexitätstheorie (DE-588)4120591-1 s 1\p DE-604 Digraph (DE-588)4012307-8 s 2\p DE-604 Gutin, Gregory Z. 1957- Verfasser (DE-588)142715557 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016156075&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bang-Jensen, Jørgen 1960- Gutin, Gregory Z. 1957- Digraphs theory, algorithms and applications Gerichteter Graph Directed graphs Graphentheorie (DE-588)4113782-6 gnd Gerichteter Graph (DE-588)4156815-1 gnd Digraph (DE-588)4012307-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4156815-1 (DE-588)4012307-8 (DE-588)4120591-1 |
| title | Digraphs theory, algorithms and applications |
| title_auth | Digraphs theory, algorithms and applications |
| title_exact_search | Digraphs theory, algorithms and applications |
| title_exact_search_txtP | Digraphs theory, algorithms and applications |
| title_full | Digraphs theory, algorithms and applications Jørgen Bang-Jensen and Gregory Gutin |
| title_fullStr | Digraphs theory, algorithms and applications Jørgen Bang-Jensen and Gregory Gutin |
| title_full_unstemmed | Digraphs theory, algorithms and applications Jørgen Bang-Jensen and Gregory Gutin |
| title_short | Digraphs |
| title_sort | digraphs theory algorithms and applications |
| title_sub | theory, algorithms and applications |
| topic | Gerichteter Graph Directed graphs Graphentheorie (DE-588)4113782-6 gnd Gerichteter Graph (DE-588)4156815-1 gnd Digraph (DE-588)4012307-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Gerichteter Graph Directed graphs Graphentheorie Digraph Komplexitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016156075&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bangjensenjørgen digraphstheoryalgorithmsandapplications AT gutingregoryz digraphstheoryalgorithmsandapplications |