On directed local chromatic number, shift graphs, and Borsuk-like graphs

Gábor Simonyi, G. Tardos

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We investigate the local chromatic number of shift graphs and prove that it is close to their chromatic number. This implies that the gap between the directed local chromatic number of an oriented graph and the local chromatic number of the underlying undirected graph can be arbitrarily large. We also investigate the minimum possible directed local chromatic number of oriented versions of "topologically t-chromatic" graphs. We show that this minimum for large enough t-chromatic Schrijver graphs and t-chromatic generalized Mycielski graphs of appropriate parameters is ⌈t/4⌉+1.

Original languageEnglish
Pages (from-to)65-82
Number of pages18
JournalJournal of Graph Theory
Volume66
Issue number1
DOIs
Publication statusPublished - Jan 2011

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Keywords

  • local chromatic number
  • Schrijver graph
  • shift graph
  • topological method

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

On directed local chromatic number, shift graphs, and Borsuk-like graphs. / Simonyi, Gábor; Tardos, G.

In: Journal of Graph Theory, Vol. 66, No. 1, 01.2011, p. 65-82.

Research output: Contribution to journalArticle

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