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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)
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Title
| - Large monochromatic components in two-colored grids
- Velké jednobarevné komponenty v 2-obarvených grafech (cs)
- Large monochromatic components in two-colored grids (en)
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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)
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skos:notation
| - RIV/00216208:11320/07:00004976!RIV08-MSM-11320___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(1M0545), P(GD201/05/H014), Z(MSM0021620838)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/07:00004976
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Large; monochromatic; components; two-colored; grids (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Electronic Notes in Discrete Mathematics
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Matoušek, Jiří
- Přívětivý, Aleš
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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