Matching minors in bipartite graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Universitätsverlag der TU Berlin
2022
|
| Schriftenreihe: | Foundations of Computing
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 463 Seiten Illustrationen 21 cm x 14.8 cm, 995 g |
| ISBN: | 9783798332522 3798332525 |
Internformat
MARC
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|---|---|---|---|
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| 003 | DE-604 | ||
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| 015 | |a 22,N17 |2 dnb | ||
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| 020 | |a 9783798332522 |c Broschur : EUR 25.00 (DE), EUR 25.70 (AT) |9 978-3-7983-3252-2 | ||
| 020 | |a 3798332525 |9 3-7983-3252-5 | ||
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| 049 | |a DE-83 | ||
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| 100 | 1 | |a Wiederrecht, Sebastian |e Verfasser |0 (DE-588)1256376868 |4 aut | |
| 245 | 1 | 0 | |a Matching minors in bipartite graphs |c Sebastian Wiederrecht |
| 263 | |a 202204 | ||
| 264 | 1 | |a Berlin |b Universitätsverlag der TU Berlin |c 2022 | |
| 300 | |a XVII, 463 Seiten |b Illustrationen |c 21 cm x 14.8 cm, 995 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Foundations of Computing |v 16 | |
| 502 | |b Dissertation |c Technische Universität Berlin |d 2021 | ||
| 650 | 0 | 7 | |a Bipartiter Graph |0 (DE-588)4145661-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matching |g Graphentheorie |0 (DE-588)4831446-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Minor |g Graphentheorie |0 (DE-588)4694399-7 |2 gnd |9 rswk-swf |
| 653 | |a matching minor | ||
| 653 | |a structural graph theory | ||
| 653 | |a bipartite | ||
| 653 | |a perfect matching | ||
| 653 | |a Matching Minor | ||
| 653 | |a strukturelle Graphentheorie | ||
| 653 | |a Bipartit | ||
| 653 | |a perfektes Matching | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Bipartiter Graph |0 (DE-588)4145661-0 |D s |
| 689 | 0 | 1 | |a Minor |g Graphentheorie |0 (DE-588)4694399-7 |D s |
| 689 | 0 | 2 | |a Matching |g Graphentheorie |0 (DE-588)4831446-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 710 | 2 | |a Technische Universität Berlin |b Universitätsbibliothek |0 (DE-588)5053182-7 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-7983-3253-9 |
| 830 | 0 | |a Foundations of Computing |v 16 |w (DE-604)BV042337479 |9 16 | |
| 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=033340558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-033340558 | ||
| 883 | 1 | |8 1\p |a vlb |d 20220420 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
Datensatz im Suchindex
| _version_ | 1804183647721357312 |
|---|---|
| adam_text | CONTENTS
1.
INTRODUCTION
1
1.
BACKGROUND
9
2.
GENERAL
BACKGROUND
11
2.1.
GENERAL
GRAPH
THEORY
...................................................
12
2.2.
THE
GRAPH
MINORS
SERIES
...................................................
15
2.2.1.
TREEWIDTH
AND
DUALITY
........................................
19
2.2.2.
GRAPHS
EXCLUDING
A
MINOR
...................................
27
2.2.3.
ALGORITHMIC
PROPERTIES,
DISJOINT
PATHS,
AND
MINOR
TESTING
...................................................................
31
2.3.
STRUCTURAL
DIGRAPH
THEORY
..............................................
32
2.3.1.
GENERALISING
TREEWIDTH
........................................
36
2.3.2.
DIRECTED
TREEWIDTH
AND
DUALITY
.........................
38
2.3.3.
DISJOINT
PATHS
AND
BUTTERFLY
MINOR
TESTING
.
.
44
2.3.4.
OTHER
DIRECTED
WIDTH
PARAMETERS
...................
47
2.3.5.
ON
THE
ALGORITHMIC
POWER
OF
DIRECTED
WIDTH
MEA
SURES
..........................................................
48
3.
AN
INTRODUCTION
TO
MATCHING
THEORY
49
3.1.
GENERAL
MATCHING
THEORETIC
BACKGROUND
.....................
52
3.1.1.
FUNDAMENTAL
DECOMPOSITIONS
...........................
57
3.1.2.
BRACES
AND
BIPARTITE
GRAPHS
...............................
89
3.1.3.
BRICKS
AND
NON-BIPARTITE
GRAPHS
.....................
94
3.1.4.
MATCHING
MINORS
.................................................
104
3.2.
PERFECT
MATCHINGS,
DIGRAPHS,
AND
BIDIRECTED
GRAPHS
.
ILL
3.3.
POLYA
S
PERMANENT
PROBLEM
AND
PFAFFIAN
GRAPHS
.
.
.
124
3.4.
DIFFERENCES
BETWEEN
BIPARTITE
AND
NON-BIPARTITE
GRAPHS
131
3.5.
A
LIST
OF
OPEN
QUESTIONS
..............................................
135
CONTENTS
II.
A
MATCHING
THEORETIC
MINORS
PROJECT
139
4.
THE
TWO
PATHS
THEOREM
141
4.1.
MATCHING
CROSSES
IN
PLANAR
BRACES
...............................
146
4.2.
PATHS
AND
MATCHING
CROSSES
THROUGH
4-CYCLE
SUMS
.
.
153
4.3.
MATCHING
CROSSES
IN
PFAFFIAN
BRACES
...............................
157
4.4.
MATCHING
CROSSES
IN
NON-PFAFFIAN
BRACES
......................
175
4.5.
AN
ALGORITHM
FOR
2-MLP
.................................................
193
5.
PERFECT
MATCHING
WIDTH
203
5.1.
INTRODUCING
PERFECT
MATCHING
WIDTH
................................
203
5.1.1.
BASIC
PROPERTIES
OF
PERFECT
MATCHING
WIDTH
.
.
207
5.2.
BRACES
OF
PERFECT
MATCHING
WIDTH
2
219
5.2.1.
COMPUTING
PERFECT
MATCHING
DECOMPOSITIONS
OF
WIDTH
2
231
5.2.2.
BIPARTITE
MATCHING
COVERED
GRAPHS
OF
M-WIDTH
2
235
5.2.3.
LINEAR
PERFECT
MATCHING
WIDTH
...........................
239
5.3.
DUALITY
AND
DIRECTED
TREEWIDTH
.........................................
241
5.3.1.
EDGE
CUTS
AND
SEPARATORS
......................................
241
5.3.2.
CYCLEWIDTH
AND
DIRECTED
BRANCHWIDTH
................
247
5.3.3.
THE
BIPARTITE
MATCHING
GRID
THEOREM
................
258
5.4.
THE
DISJOINT
PATHS
PROBLEM
ON
BIPARTITE
GRAPHS
OF
BOUNDED
WIDTH
....................................................................
266
5.4.1.
COMPUTING
A
PERFECT
MATCHING
DECOMPOSITION
.
269
5.4.2.
THE
DYNAMIC
PROGRAMMING
FOR
BIPARTITE
FE-DAPP
277
5.5.
PERFECT
MATCHING
WIDTH
AND
TREEWIDTH
.............................
285
6.
TANGLES
AND
A
UNIFIED
DECOMPOSITION
287
6.1.
BLOCKAGES
AND
STRICT
LINEAR
PERFECT
MATCHING
WIDTH
.
288
6.1.1.
ORDERED
LINEAR
PERFECT
MATCHING
WIDTH
....
289
6.1.2.
W-BLOCKAGES
AND
T^-PATHS
OF
ACCURACY
CJ
....
296
6.2.
GENERALISED
TIGHT
CUTS
AND
DIRECTED
SEPARATIONS
.
.
.
301
6.3.
TANGLES
AND
A
UNIFIED
WIDTH
MEASURE
.............................
314
6.3.1.
APPLYING
STRUCTURAL
DIGRAPH
THEORY
...................
319
7.
EXCLUDING
A
PLANAR
MATCHING
MINOR
329
7.1.
PLANAR
MATCHING
COVERED
GRAPHS
IN
GRIDS
.....................
330
XVI
CONTENTS
7.2.
DIGRAPHS
AND
ERDOS-POSA
FOR
BUTTERFLY
MINOR
ANTI-CHAINS
334
7.2.1.
THE
STRONG
GENUS
OF
DIGRAPHS
...............................
335
7.2.2.
ERDOS-POSA
FOR
ANTI-CHAINS
..................................
342
7.3.
MATCHING
MINORS
AND
THE
ERDOS-POSA
PROPERTY
....
346
8.
A
WEAK
STRUCTURE
THEOREM
353
8.1.
DESCRIBING
AND
SUBDIVIDING
A
WALL
..................................
363
8.2.
STEP
1:
REMOVE
LONG
JUMPS
..............................................
370
8.3.
STEP
2:
CROSSES
AND
BIPARTITE
NON-PFAFFIAN
GRAPHS
.
.
378
8.4.
PROOF
OF
THE
BIPARTITE
FLAT
WALL
THEOREM
FOR
MATCHING
MINORS
...................................................................................
394
8.5.
APPLICATIONS
TO
STRUCTURAL
(DI)GRAPH
THEORY
................
410
8.5.1.
ANOTHER
FLAT
WALL
THEOREM
FOR
DIGRAPHS
....
411
8.5.2.
AN
APPLICATION
TO
TREEWIDTH
OF
UNDIRECTED
GRAPHS
413
III.
CONCLUSION
419
9.
CONCLUDING
REMARKS
421
9.1.
THE
MATCHING
CHROMATIC
NUMBER
.....................................
422
9.2.
BEYOND
BIPARTITE:
BIDIRECTED
GRAPHS
...............................
424
9.2.1.
DIFFERENT
NOTIONS
OF
STRONG
CONNECTIVITY
.
.
.
426
9.2.2.
STRONGLY
CONNECTED
BIDIRECTED
GRAPHS
................
430
9.2.3.
BIDIRECTED
TREEWIDTH
..............................................
432
9.2.4.
BARRIERS,
STRONG
COMPONENTS,
AND
CYCLE
POROSITY
440
9.3.
REGARDING
OUR
LIST
OF
OPEN
QUESTIONS
............................
445
XVII
|
| adam_txt |
CONTENTS
1.
INTRODUCTION
1
1.
BACKGROUND
9
2.
GENERAL
BACKGROUND
11
2.1.
GENERAL
GRAPH
THEORY
.
12
2.2.
THE
GRAPH
MINORS
SERIES
.
15
2.2.1.
TREEWIDTH
AND
DUALITY
.
19
2.2.2.
GRAPHS
EXCLUDING
A
MINOR
.
27
2.2.3.
ALGORITHMIC
PROPERTIES,
DISJOINT
PATHS,
AND
MINOR
TESTING
.
31
2.3.
STRUCTURAL
DIGRAPH
THEORY
.
32
2.3.1.
GENERALISING
TREEWIDTH
.
36
2.3.2.
DIRECTED
TREEWIDTH
AND
DUALITY
.
38
2.3.3.
DISJOINT
PATHS
AND
BUTTERFLY
MINOR
TESTING
.
.
44
2.3.4.
OTHER
DIRECTED
WIDTH
PARAMETERS
.
47
2.3.5.
ON
THE
ALGORITHMIC
POWER
OF
DIRECTED
WIDTH
MEA
SURES
.
48
3.
AN
INTRODUCTION
TO
MATCHING
THEORY
49
3.1.
GENERAL
MATCHING
THEORETIC
BACKGROUND
.
52
3.1.1.
FUNDAMENTAL
DECOMPOSITIONS
.
57
3.1.2.
BRACES
AND
BIPARTITE
GRAPHS
.
89
3.1.3.
BRICKS
AND
NON-BIPARTITE
GRAPHS
.
94
3.1.4.
MATCHING
MINORS
.
104
3.2.
PERFECT
MATCHINGS,
DIGRAPHS,
AND
BIDIRECTED
GRAPHS
.
ILL
3.3.
POLYA
'
S
PERMANENT
PROBLEM
AND
PFAFFIAN
GRAPHS
.
.
.
124
3.4.
DIFFERENCES
BETWEEN
BIPARTITE
AND
NON-BIPARTITE
GRAPHS
131
3.5.
A
LIST
OF
OPEN
QUESTIONS
.
135
CONTENTS
II.
A
MATCHING
THEORETIC
MINORS
PROJECT
139
4.
THE
TWO
PATHS
THEOREM
141
4.1.
MATCHING
CROSSES
IN
PLANAR
BRACES
.
146
4.2.
PATHS
AND
MATCHING
CROSSES
THROUGH
4-CYCLE
SUMS
.
.
153
4.3.
MATCHING
CROSSES
IN
PFAFFIAN
BRACES
.
157
4.4.
MATCHING
CROSSES
IN
NON-PFAFFIAN
BRACES
.
175
4.5.
AN
ALGORITHM
FOR
2-MLP
.
193
5.
PERFECT
MATCHING
WIDTH
203
5.1.
INTRODUCING
PERFECT
MATCHING
WIDTH
.
203
5.1.1.
BASIC
PROPERTIES
OF
PERFECT
MATCHING
WIDTH
.
.
207
5.2.
BRACES
OF
PERFECT
MATCHING
WIDTH
2
219
5.2.1.
COMPUTING
PERFECT
MATCHING
DECOMPOSITIONS
OF
WIDTH
2
231
5.2.2.
BIPARTITE
MATCHING
COVERED
GRAPHS
OF
M-WIDTH
2
235
5.2.3.
LINEAR
PERFECT
MATCHING
WIDTH
.
239
5.3.
DUALITY
AND
DIRECTED
TREEWIDTH
.
241
5.3.1.
EDGE
CUTS
AND
SEPARATORS
.
241
5.3.2.
CYCLEWIDTH
AND
DIRECTED
BRANCHWIDTH
.
247
5.3.3.
THE
BIPARTITE
MATCHING
GRID
THEOREM
.
258
5.4.
THE
DISJOINT
PATHS
PROBLEM
ON
BIPARTITE
GRAPHS
OF
BOUNDED
WIDTH
.
266
5.4.1.
COMPUTING
A
PERFECT
MATCHING
DECOMPOSITION
.
269
5.4.2.
THE
DYNAMIC
PROGRAMMING
FOR
BIPARTITE
FE-DAPP
277
5.5.
PERFECT
MATCHING
WIDTH
AND
TREEWIDTH
.
285
6.
TANGLES
AND
A
UNIFIED
DECOMPOSITION
287
6.1.
BLOCKAGES
AND
STRICT
LINEAR
PERFECT
MATCHING
WIDTH
.
288
6.1.1.
ORDERED
LINEAR
PERFECT
MATCHING
WIDTH
.
289
6.1.2.
W-BLOCKAGES
AND
T^-PATHS
OF
ACCURACY
CJ
.
296
6.2.
GENERALISED
TIGHT
CUTS
AND
DIRECTED
SEPARATIONS
.
.
.
301
6.3.
TANGLES
AND
A
UNIFIED
WIDTH
MEASURE
.
314
6.3.1.
APPLYING
STRUCTURAL
DIGRAPH
THEORY
.
319
7.
EXCLUDING
A
PLANAR
MATCHING
MINOR
329
7.1.
PLANAR
MATCHING
COVERED
GRAPHS
IN
GRIDS
.
330
XVI
CONTENTS
7.2.
DIGRAPHS
AND
ERDOS-POSA
FOR
BUTTERFLY
MINOR
ANTI-CHAINS
334
7.2.1.
THE
STRONG
GENUS
OF
DIGRAPHS
.
335
7.2.2.
ERDOS-POSA
FOR
ANTI-CHAINS
.
342
7.3.
MATCHING
MINORS
AND
THE
ERDOS-POSA
PROPERTY
.
346
8.
A
WEAK
STRUCTURE
THEOREM
353
8.1.
DESCRIBING
AND
SUBDIVIDING
A
WALL
.
363
8.2.
STEP
1:
REMOVE
LONG
JUMPS
.
370
8.3.
STEP
2:
CROSSES
AND
BIPARTITE
NON-PFAFFIAN
GRAPHS
.
.
378
8.4.
PROOF
OF
THE
BIPARTITE
FLAT
WALL
THEOREM
FOR
MATCHING
MINORS
.
394
8.5.
APPLICATIONS
TO
STRUCTURAL
(DI)GRAPH
THEORY
.
410
8.5.1.
ANOTHER
FLAT
WALL
THEOREM
FOR
DIGRAPHS
.
411
8.5.2.
AN
APPLICATION
TO
TREEWIDTH
OF
UNDIRECTED
GRAPHS
413
III.
CONCLUSION
419
9.
CONCLUDING
REMARKS
421
9.1.
THE
MATCHING
CHROMATIC
NUMBER
.
422
9.2.
BEYOND
BIPARTITE:
BIDIRECTED
GRAPHS
.
424
9.2.1.
DIFFERENT
NOTIONS
OF
'
STRONG
CONNECTIVITY
'
.
.
.
426
9.2.2.
STRONGLY
CONNECTED
BIDIRECTED
GRAPHS
.
430
9.2.3.
BIDIRECTED
TREEWIDTH
.
432
9.2.4.
BARRIERS,
STRONG
COMPONENTS,
AND
CYCLE
POROSITY
440
9.3.
REGARDING
OUR
LIST
OF
OPEN
QUESTIONS
.
445
XVII |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Wiederrecht, Sebastian |
| author_GND | (DE-588)1256376868 |
| author_facet | Wiederrecht, Sebastian |
| author_role | aut |
| author_sort | Wiederrecht, Sebastian |
| author_variant | s w sw |
| building | Verbundindex |
| bvnumber | BV047959302 |
| ctrlnum | (OCoLC)1314908667 (DE-599)DNB1255717270 |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV047959302 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:40:00Z |
| indexdate | 2024-07-10T09:26:46Z |
| institution | BVB |
| institution_GND | (DE-588)5053182-7 |
| isbn | 9783798332522 3798332525 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033340558 |
| oclc_num | 1314908667 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XVII, 463 Seiten Illustrationen 21 cm x 14.8 cm, 995 g |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Universitätsverlag der TU Berlin |
| record_format | marc |
| series | Foundations of Computing |
| series2 | Foundations of Computing |
| spelling | Wiederrecht, Sebastian Verfasser (DE-588)1256376868 aut Matching minors in bipartite graphs Sebastian Wiederrecht 202204 Berlin Universitätsverlag der TU Berlin 2022 XVII, 463 Seiten Illustrationen 21 cm x 14.8 cm, 995 g txt rdacontent n rdamedia nc rdacarrier Foundations of Computing 16 Dissertation Technische Universität Berlin 2021 Bipartiter Graph (DE-588)4145661-0 gnd rswk-swf Matching Graphentheorie (DE-588)4831446-8 gnd rswk-swf Minor Graphentheorie (DE-588)4694399-7 gnd rswk-swf matching minor structural graph theory bipartite perfect matching Matching Minor strukturelle Graphentheorie Bipartit perfektes Matching (DE-588)4113937-9 Hochschulschrift gnd-content Bipartiter Graph (DE-588)4145661-0 s Minor Graphentheorie (DE-588)4694399-7 s Matching Graphentheorie (DE-588)4831446-8 s DE-604 Technische Universität Berlin Universitätsbibliothek (DE-588)5053182-7 pbl Erscheint auch als Online-Ausgabe 978-3-7983-3253-9 Foundations of Computing 16 (DE-604)BV042337479 16 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033340558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20220420 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Wiederrecht, Sebastian Matching minors in bipartite graphs Foundations of Computing Bipartiter Graph (DE-588)4145661-0 gnd Matching Graphentheorie (DE-588)4831446-8 gnd Minor Graphentheorie (DE-588)4694399-7 gnd |
| subject_GND | (DE-588)4145661-0 (DE-588)4831446-8 (DE-588)4694399-7 (DE-588)4113937-9 |
| title | Matching minors in bipartite graphs |
| title_auth | Matching minors in bipartite graphs |
| title_exact_search | Matching minors in bipartite graphs |
| title_exact_search_txtP | Matching minors in bipartite graphs |
| title_full | Matching minors in bipartite graphs Sebastian Wiederrecht |
| title_fullStr | Matching minors in bipartite graphs Sebastian Wiederrecht |
| title_full_unstemmed | Matching minors in bipartite graphs Sebastian Wiederrecht |
| title_short | Matching minors in bipartite graphs |
| title_sort | matching minors in bipartite graphs |
| topic | Bipartiter Graph (DE-588)4145661-0 gnd Matching Graphentheorie (DE-588)4831446-8 gnd Minor Graphentheorie (DE-588)4694399-7 gnd |
| topic_facet | Bipartiter Graph Matching Graphentheorie Minor Graphentheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033340558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042337479 |
| work_keys_str_mv | AT wiederrechtsebastian matchingminorsinbipartitegraphs AT technischeuniversitatberlinuniversitatsbibliothek matchingminorsinbipartitegraphs |