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Large monochromatic components in two-colored grids

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F07%3A00004976" target="_blank" >RIV/00216208:11320/07:00004976 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Large monochromatic components in two-colored grids

  • Original language description

    (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.

  • Czech name

    Velké jednobarevné komponenty v 2-obarvených grafech

  • Czech 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.

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2007

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Electronic Notes in Discrete Mathematics

  • ISSN

    1571-0653

  • e-ISSN

  • Volume of the periodical

    29

  • Issue of the periodical within the volume

    C

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    7

  • Pages from-to

    3-9

  • UT code for WoS article

  • EID of the result in the Scopus database