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  • 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. (en)
Title
  • Stars and Bonds in Crossing-Critical Graphs
  • Stars and Bonds in Crossing-Critical Graphs (en)
skos:prefLabel
  • Stars and Bonds in Crossing-Critical Graphs
  • Stars and Bonds in Crossing-Critical Graphs (en)
skos:notation
  • RIV/00216224:14330/08:00024776!RIV10-GA0-14330___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/08/0308)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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http://linked.open...dnocenehoVysledku
  • 397227
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14330/08:00024776
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  • crossing number; crossing-critical graph (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • FR - Francouzská republika
http://linked.open...ontrolniKodProRIV
  • [360E633C6981]
http://linked.open...i/riv/nazevZdroje
  • Electronic Notes in Discrete Mathematics
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 31
http://linked.open...iv/tvurceVysledku
  • Hliněný, Petr
  • Salazar, Gelasio
issn
  • 1571-0653
number of pages
http://localhost/t...ganizacniJednotka
  • 14330
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