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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

On Minimal Triangle-Free \(5\)-Chromatic Graphs

Charles M. Grinstead1, Matthew Katinsky1, David Van Stone1
1Department of Mathematics Swarthmore College Swarthmore, PA 19081 U.S.A.
  • Published: 31/10/1989

Abstract

Avis has shown that the number of vertices of a minimal triangle-free \(5\)-chromatic graph is no fewer than \(19\). Mycielski has shown that this number is no more than \(23\). In this paper, we improve these bounds to \(21\) and \(22\), respectively.

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Citation
Charles M. Grinstead, Matthew Katinsky, David Van Stone. On Minimal Triangle-Free \(5\)-Chromatic Graphs[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 006. 189-193. DOI: .