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Description
  • We show that if G is a 4-critical graph embedded in a fixed surface S so that every contractible cycle has length at least 5, then G can be expressed as G = G'boolean OR G(1)boolean OR G(2)boolean OR ... boolean OR G(k), where vertical bar V (C')vertical bar| and k are bounded by a constant (depending linearly on the genus of Sigma) and C-1, ... , C-k are graphs (of unbounded size) whose structure we describe exactly. The proof is computer assisted-we use a computer to enumerate all plane 4-critical graphs of girth 5 with a precolored cycle of length at most 16 that are used in the basic case of the inductive proof of the statement.
  • We show that if G is a 4-critical graph embedded in a fixed surface S so that every contractible cycle has length at least 5, then G can be expressed as G = G'boolean OR G(1)boolean OR G(2)boolean OR ... boolean OR G(k), where vertical bar V (C')vertical bar| and k are bounded by a constant (depending linearly on the genus of Sigma) and C-1, ... , C-k are graphs (of unbounded size) whose structure we describe exactly. The proof is computer assisted-we use a computer to enumerate all plane 4-critical graphs of girth 5 with a precolored cycle of length at most 16 that are used in the basic case of the inductive proof of the statement. (en)
Title
  • 4-CRITICAL GRAPHS ON SURFACES WITHOUT CONTRACTIBLE ({= 4)-CYCLES
  • 4-CRITICAL GRAPHS ON SURFACES WITHOUT CONTRACTIBLE ({= 4)-CYCLES (en)
skos:prefLabel
  • 4-CRITICAL GRAPHS ON SURFACES WITHOUT CONTRACTIBLE ({= 4)-CYCLES
  • 4-CRITICAL GRAPHS ON SURFACES WITHOUT CONTRACTIBLE ({= 4)-CYCLES (en)
skos:notation
  • RIV/00216208:11320/14:10283293!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GBP202/12/G061), P(LH12095)
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
  • 58290
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/14:10283293
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • graphs of surfaces; contractible cycles; graph coloring (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [32E08B6EAF30]
http://linked.open...i/riv/nazevZdroje
  • SIAM Journal on Discrete Mathematics
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
  • 28
http://linked.open...iv/tvurceVysledku
  • Dvořák, Zdeněk
  • Lidický, Bernard
http://linked.open...ain/vavai/riv/wos
  • 000333685700036
issn
  • 0895-4801
number of pages
http://bibframe.org/vocab/doi
  • 10.1137/130920952
http://localhost/t...ganizacniJednotka
  • 11320
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