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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F07%3A00024653%21RIV10-GA0-14330___
rdf:type
skos:Concept n13: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 $5$ 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 $\big[4,6-\frac8{k+1}\big)$.
dcterms:title
New almost-planar crossing-critical graph families New almost-planar crossing-critical graph families
skos:prefLabel
New almost-planar crossing-critical graph families New almost-planar crossing-critical graph families
skos:notation
RIV/00216224:14330/07:00024653!RIV10-GA0-14330___
n4:aktivita
n9:P
n4:aktivity
P(GA201/05/0050)
n4:dodaniDat
n5:2010
n4:domaciTvurceVysledku
n16:7595646
n4:druhVysledku
n11:O
n4:duvernostUdaju
n15:S
n4:entitaPredkladatele
n14:predkladatel
n4:idSjednocenehoVysledku
437061
n4:idVysledku
RIV/00216224:14330/07:00024653
n4:jazykVysledku
n17:eng
n4:klicovaSlova
graph; crossing number; crossing-critical
n4:klicoveSlovo
n8:crossing-critical n8:graph n8:crossing%20number
n4:kontrolniKodProRIV
[28C4EB88890F]
n4:obor
n10:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:projekt
n7:GA201%2F05%2F0050
n4:rokUplatneniVysledku
n5:2007
n4:tvurceVysledku
Hliněný, Petr
n12:organizacniJednotka
14330