About: New almost-planar crossing-critical graph families

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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 $5$ in crossing-critical graphs remains open. Furthermore, our 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 $\big[4,6-\frac8{k+1}\big)$. 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 $5$ in crossing-critical graphs remains open. Furthermore, our 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 $\big[4,6-\frac8{k+1}\big)$. (en)
Title	New almost-planar crossing-critical graph families New almost-planar crossing-critical graph families (en)
skos:prefLabel	New almost-planar crossing-critical graph families New almost-planar crossing-critical graph families (en)
skos:notation	RIV/00216224:14330/07:00024653!RIV10-GA0-14330___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA201/05/0050)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Hliněný, Petr
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
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	437061
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/07:00024653
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	graph; crossing number; crossing-critical (en)
http://linked.open.../riv/klicoveSlovo	graph crossing number crossing-critical
http://linked.open...ontrolniKodProRIV	[28C4EB88890F]
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	Structural properties and algorithmic complexity of discrete problems
http://linked.open...UplatneniVysledku	2007
http://linked.open...iv/tvurceVysledku	Hliněný, Petr
http://localhost/t...ganizacniJednotka	14330

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