About: New infinite families of almost-planar crossing-critical graphs     Goto   Sponge   NotDistinct   Permalink

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  • 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 $\big[3+\frac15,6-\frac8{k+1}\big)$. (en)
Title
  • New infinite families of almost-planar crossing-critical graphs
  • New infinite families of almost-planar crossing-critical graphs (en)
skos:prefLabel
  • New infinite families of almost-planar crossing-critical graphs
  • New infinite families of almost-planar crossing-critical graphs (en)
skos:notation
  • RIV/00216224:14330/08:00025241!RIV10-GA0-14330___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), P(GA201/08/0308), S
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 382567
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14330/08:00025241
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • crossing-critical; graph (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [33141A40BB9A]
http://linked.open...i/riv/nazevZdroje
  • Electronic Journal of Combinatorics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 15
http://linked.open...iv/tvurceVysledku
  • Hliněný, Petr
http://linked.open...ain/vavai/riv/wos
  • 000258122700003
issn
  • 1077-8926
number of pages
http://localhost/t...ganizacniJednotka
  • 14330
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