About: New infinite families of almost-planar crossing-critical graphs

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About: New infinite families of almost-planar crossing-critical graphs Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We show that, for all choices of integers $k>2$ and $m$, there are simple $3$-connected $k$-crossing-critical graphs containing more than $m$ vertices of each even degree $\leq2k-2$. This construction answers one half of a question raised by Bokal, while the other half asking analogously about vertices of odd degrees at least $7$ in crossing-critical graphs remains open. Furthermore, our newly constructed graphs have several other interesting properties; for instance, they are almost planar and their average degree can attain any rational value in the interval $\big[3+\frac15,6-\frac8{k+1}\big)$. We show that, for all choices of integers $k>2$ and $m$, there are simple $3$-connected $k$-crossing-critical graphs containing more than $m$ vertices of each even degree $\leq2k-2$. This construction answers one half of a question raised by Bokal, while the other half asking analogously about vertices of odd degrees at least $7$ in crossing-critical graphs remains open. Furthermore, our newly constructed graphs have several other interesting properties; for instance, they are almost planar and their average degree can attain any rational value in the interval $\big[3+\frac15,6-\frac8{k+1}\big)$. (en)
Title	New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs (en)
skos:prefLabel	New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs (en)
skos:notation	RIV/00216224:14330/08:00025241!RIV10-GA0-14330___
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(1M0545), P(GA201/08/0308), S
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Hliněný, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
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	382567
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/08:00025241
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	crossing-critical; graph (en)
http://linked.open.../riv/klicoveSlovo	graph crossing-critical
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[33141A40BB9A]
http://linked.open...i/riv/nazevZdroje	Electronic Journal of Combinatorics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science Utilization of structural and %22Width%22 parameters in combinatorics and algorithmic complexity
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	15
http://linked.open...iv/tvurceVysledku	Hliněný, Petr
http://linked.open...ain/vavai/riv/wos	000258122700003
issn	1077-8926
number of pages	12 (xsd:int)
http://localhost/t...ganizacniJednotka	14330
is http://linked.open...avai/riv/vysledek of	New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs

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