About: Stars and Bonds in Crossing-Critical Graphs

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The structure of all known infinite families of crossing--critical graphs has led to the conjecture that crossing--critical graphs have bounded bandwidth. If true, this would imply that crossing--critical graphs have bounded degree, that is, that they cannot contain subdivisions of $K_{1,n}$ for arbitrarily large $n$. In this paper we prove two results that revolve around this conjecture. On the positive side, we show that crossing--critical graphs cannot contain subdivisions of $K_{2,n}$ for arbitrarily large $n$. On the negative side, we show that there are graphs with arbitrarily large maximum degree that are $2$-crossing--critical in the projective plane. The structure of all known infinite families of crossing--critical graphs has led to the conjecture that crossing--critical graphs have bounded bandwidth. If true, this would imply that crossing--critical graphs have bounded degree, that is, that they cannot contain subdivisions of $K_{1,n}$ for arbitrarily large $n$. In this paper we prove two results that revolve around this conjecture. On the positive side, we show that crossing--critical graphs cannot contain subdivisions of $K_{2,n}$ for arbitrarily large $n$. On the negative side, we show that there are graphs with arbitrarily large maximum degree that are $2$-crossing--critical in the projective plane. (en) Prezentujeme dva přístupy k dosud otevřené domněnce, že průsečíkově kritické grafy mají omezený maximální stupeň. Na pozitivní straně dokazujeme, že tyto grafy nemohou obsahovat subdivizi velkého K_2,n, ale na negativní straně ukazujeme neplatnost domněnky v projektivní rovině. (cs)
Title	Stars and Bonds in Crossing-Critical Graphs Stars and Bonds in Crossing-Critical Graphs (en) Hvězdy a řezy v průsečíkově kritických grafech (cs)
skos:prefLabel	Stars and Bonds in Crossing-Critical Graphs Stars and Bonds in Crossing-Critical Graphs (en) Hvězdy a řezy v průsečíkově kritických grafech (cs)
skos:notation	RIV/00216224:14330/08:00024776!RIV09-GA0-14330___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA201/08/0308)
http://linked.open...vai/riv/dodaniDat	2009
http://linked.open...aciTvurceVysledku	Hliněný, Petr
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Fakulta informatiky
http://linked.open...dnocenehoVysledku	397228
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/08:00024776
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	crossing number; crossing-critical graph (en)
http://linked.open.../riv/klicoveSlovo	crossing number crossing-critical graph
http://linked.open...ontrolniKodProRIV	[E43AFB9045A9]
http://linked.open...v/mistoKonaniAkce	Paris, France
http://linked.open...i/riv/mistoVydani	Nizozemi
http://linked.open...i/riv/nazevZdroje	The International Conference on Topological and Geometric Graph Theory TGGT2008, Electronic Notes in Discrete Mathematics 31, 2008
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Utilization of structural and %22Width%22 parameters in combinatorics and algorithmic complexity
http://linked.open...UplatneniVysledku	2008
http://linked.open...iv/tvurceVysledku	Hliněný, Petr Salazar, Gelasio
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2008-05-19 (xsd:date)
issn	1571-0653
number of pages	5 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Elsevier
http://localhost/t...ganizacniJednotka	14330

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