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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F08%3A00024776%21RIV10-GA0-14330___
rdf:type
n6:Vysledek skos:Concept
dcterms: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.
dcterms:title
Stars and Bonds in Crossing-Critical Graphs Stars and Bonds in Crossing-Critical Graphs
skos:prefLabel
Stars and Bonds in Crossing-Critical Graphs Stars and Bonds in Crossing-Critical Graphs
skos:notation
RIV/00216224:14330/08:00024776!RIV10-GA0-14330___
n3:aktivita
n14:P
n3:aktivity
P(GA201/08/0308)
n3:cisloPeriodika
1
n3:dodaniDat
n7:2010
n3:domaciTvurceVysledku
n11:7595646
n3:druhVysledku
n16:J
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
397227
n3:idVysledku
RIV/00216224:14330/08:00024776
n3:jazykVysledku
n5:eng
n3:klicovaSlova
crossing number; crossing-critical graph
n3:klicoveSlovo
n4:crossing-critical%20graph n4:crossing%20number
n3:kodStatuVydavatele
FR - Francouzská republika
n3:kontrolniKodProRIV
[360E633C6981]
n3:nazevZdroje
Electronic Notes in Discrete Mathematics
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n15:GA201%2F08%2F0308
n3:rokUplatneniVysledku
n7:2008
n3:svazekPeriodika
31
n3:tvurceVysledku
Salazar, Gelasio Hliněný, Petr
s:issn
1571-0653
s:numberOfPages
5
n13:organizacniJednotka
14330