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  • Considering all partitions of the edges of a graph G to k parts, the the k-chromatic number of G is is the maximum of the sum of the chromatic numbers of the parts. We derive a Heawood-type formula for the k-chromatic number of graphs embedded in a fixed surface, improving the previously known upper bounds. In infinitely many cases, the new upper bound coincides with the lower bound obtained from embedding disjoint cliques in the surface. In the proof of this result, we derive a variant of Euler's Formula for union of several graphs that might be interesting independently.
  • Considering all partitions of the edges of a graph G to k parts, the the k-chromatic number of G is is the maximum of the sum of the chromatic numbers of the parts. We derive a Heawood-type formula for the k-chromatic number of graphs embedded in a fixed surface, improving the previously known upper bounds. In infinitely many cases, the new upper bound coincides with the lower bound obtained from embedding disjoint cliques in the surface. In the proof of this result, we derive a variant of Euler's Formula for union of several graphs that might be interesting independently. (en)
Title
  • $k$-chromatic number of graphs on surfaces
  • $k$-chromatic number of graphs on surfaces (en)
skos:prefLabel
  • $k$-chromatic number of graphs on surfaces
  • $k$-chromatic number of graphs on surfaces (en)
skos:notation
  • RIV/00216208:11320/09:00207123!RIV10-MSM-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), P(MEB090805)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 321634
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/09:00207123
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • $k$-chromatic; number; graphs; surfaces (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [D3D140D6E43A]
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
  • 23
http://linked.open...iv/tvurceVysledku
  • Dvořák, Zdeněk
  • Škrekovski, Riste
http://linked.open...ain/vavai/riv/wos
  • 000263103400034
issn
  • 0895-4801
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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