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Description
  • (Tento článek je konferenční abstrakt) Uvažuje se d-dimenzionální mříška s diagonálami, což je graf, jehož vrcholy jsou všechny d-tice se složkami z množiny {1,2,...,n} a dvě d-tice jsou spojené hranou, pokud se liší v každé složce nejvýš o 1. Dokazuje se, že pro každé obarvení vrcholů 2 barvami existuje souvislý jednobarevný podgraf s minimálně n^(d-1)-O(n^(d-2)) vrcholy, což je téměř nejlepší možný výsledek. Podobný problém se řeší také pro grafy triangulovaných mřížek. (cs)
  • (This paper is an extended abstract) We consider the d-dimensional grid with diagonals, which is the graph whose vertices are d-component vectors with components from {1,2,...,n} and edges connecting every two vertices that differ by at most 1 in every coordinate. We prove that whenever the vertices are colored by two colors, there exists a monochromatic connected subgraph with at leastt n^(d-1)-O(n^(d-2)) vertices, which is nearly tight. We also consider a similar problem for triangulated grids.
  • (This paper is an extended abstract) We consider the d-dimensional grid with diagonals, which is the graph whose vertices are d-component vectors with components from {1,2,...,n} and edges connecting every two vertices that differ by at most 1 in every coordinate. We prove that whenever the vertices are colored by two colors, there exists a monochromatic connected subgraph with at leastt n^(d-1)-O(n^(d-2)) vertices, which is nearly tight. We also consider a similar problem for triangulated grids. (en)
Title
  • Large monochromatic components in two-colored grids
  • Velké jednobarevné komponenty v 2-obarvených grafech (cs)
  • Large monochromatic components in two-colored grids (en)
skos:prefLabel
  • Large monochromatic components in two-colored grids
  • Velké jednobarevné komponenty v 2-obarvených grafech (cs)
  • Large monochromatic components in two-colored grids (en)
skos:notation
  • RIV/00216208:11320/07:00004976!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 3;9
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(1M0545), P(GD201/05/H014), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • C
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
  • 430550
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/07:00004976
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Large; monochromatic; components; two-colored; grids (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [048B22D60B48]
http://linked.open...i/riv/nazevZdroje
  • Electronic Notes in 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
  • 29
http://linked.open...iv/tvurceVysledku
  • Matoušek, Jiří
  • Přívětivý, Aleš
http://linked.open...n/vavai/riv/zamer
issn
  • 1571-0653
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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