Efficient graph packing via game Colouring

Henry Kierstead, A. V. Kostochka

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

The game colouring number gcol(G) of a graph G is the least k such that, if two players take turns choosing the vertices of a graph, then either of them can ensure that every vertex has fewer than k neighbours chosen before it, regardless of what choices the other player makes. Clearly gcol(G) (G)+1. Sauer and Spencer [20] proved that if two graphs G1 and G2 on n vertices satisfy 2Δ (G1)≤ Δ(G2) < n then they pack, i.e., there is an embedding of G1 into the complement of G2. We improve this by showing that if (gcol(G1)1) Δ (G2)+(gcol(G 2)1)(G1) < n then G1 and G2 pack. To our knowledge this is the first application of colouring games to a non-game problem.

Original languageEnglish (US)
Pages (from-to)765-774
Number of pages10
JournalCombinatorics Probability and Computing
Volume18
Issue number5
DOIs
StatePublished - Sep 1 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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