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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F08%3A00025241%21RIV10-GA0-14330___
rdf:type
skos:Concept n15:Vysledek
dcterms: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 $\big[3+\frac15,6-\frac8{k+1}\big)$.
dcterms:title
New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs
skos:prefLabel
New infinite families of almost-planar crossing-critical graphs New infinite families of almost-planar crossing-critical graphs
skos:notation
RIV/00216224:14330/08:00025241!RIV10-GA0-14330___
n4:aktivita
n11:S n11:P
n4:aktivity
P(1M0545), P(GA201/08/0308), S
n4:cisloPeriodika
1
n4:dodaniDat
n5:2010
n4:domaciTvurceVysledku
n8:7595646
n4:druhVysledku
n7:J
n4:duvernostUdaju
n14:S
n4:entitaPredkladatele
n12:predkladatel
n4:idSjednocenehoVysledku
382567
n4:idVysledku
RIV/00216224:14330/08:00025241
n4:jazykVysledku
n9:eng
n4:klicovaSlova
crossing-critical; graph
n4:klicoveSlovo
n13:graph n13:crossing-critical
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[33141A40BB9A]
n4:nazevZdroje
Electronic Journal of Combinatorics
n4:obor
n17:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:projekt
n16:GA201%2F08%2F0308 n16:1M0545
n4:rokUplatneniVysledku
n5:2008
n4:svazekPeriodika
15
n4:tvurceVysledku
Hliněný, Petr
n4:wos
000258122700003
s:issn
1077-8926
s:numberOfPages
12
n18:organizacniJednotka
14330