Hall ratio of the Mycielski graphs

Mathew Cropper, A. Gyárfás, Jeno Lehel

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let n (G) denote the number of vertices of a graph G and let α (G) be the independence number of G, the maximum number of pairwise nonadjacent vertices of G. The Hall ratio of a graph G is defined byρ (G) = max {} fenced(frac(n (H), α (H)) : H ⊆ G),where the maximum is taken over all induced subgraphs H of G. It is obvious that every graph G satisfies ω (G) ≤ ρ (G) ≤ χ (G) where ω and χ denote the clique number and the chromatic number of G, respectively. We show that the interval [ω (G), ρ (G)] can be arbitrary large by estimating the Hall ratio of the Mycielski graphs.

Original languageEnglish
Pages (from-to)1988-1990
Number of pages3
JournalDiscrete Mathematics
Volume306
Issue number16
DOIs
Publication statusPublished - Aug 28 2006

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Graph in graph theory
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Clique number
Independence number
Induced Subgraph
Chromatic number
Pairwise
Interval
Arbitrary
Vertex of a graph

Keywords

  • Fractional chromatic number
  • Hall ratio
  • Mycielski graphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Hall ratio of the Mycielski graphs. / Cropper, Mathew; Gyárfás, A.; Lehel, Jeno.

In: Discrete Mathematics, Vol. 306, No. 16, 28.08.2006, p. 1988-1990.

Research output: Contribution to journalArticle

Cropper, Mathew ; Gyárfás, A. ; Lehel, Jeno. / Hall ratio of the Mycielski graphs. In: Discrete Mathematics. 2006 ; Vol. 306, No. 16. pp. 1988-1990.
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