Structure and generation of crossing-critical graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385421" target="_blank" >RIV/00216208:11320/18:10385421 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14330/18:00101458
Result on the web
<a href="http://drops.dagstuhl.de/opus/volltexte/2018/8746" target="_blank" >http://drops.dagstuhl.de/opus/volltexte/2018/8746</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2018.33" target="_blank" >10.4230/LIPIcs.SoCG.2018.33</a>

Result language
angličtina
Original language name
Structure and generation of crossing-critical graphs
Original language description
We study c-crossing-critical graphs, which are the minimal graphs that require at least c edge-crossings when drawn in the plane. For c=1 there are only two such graphs without degree-2 vertices, K_5 and K_{3,3}, but for any fixed c>1 there exist infinitely many c-crossing-critical graphs. It has been previously shown that c-crossing-critical graphs have bounded path-width and contain only a bounded number of internally disjoint paths between any two vertices. We expand on these results, providing a more detailed description of the structure of crossing-critical graphs. On the way towards this description, we prove a new structural characterisation of plane graphs of bounded path-width. Then we show that every c-crossing-critical graph can be obtained from a c-crossing-critical graph of bounded size by replicating bounded-size parts that already appear in narrow "bands" or "fans" in the graph. This also gives an algorithm to generate all the c-crossing-critical graphs of at most given order n in polynomial time per each generated graph.
Czech name
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Czech description
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Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
34th International Symposium on Computational Geometry (SoCG 2018)
ISBN
978-3-95977-066-8
ISSN
1868-8969
e-ISSN
neuvedeno
Number of pages
14
Pages from-to
1-14
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Budapest, Hungary
Event date
Jun 11, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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