A note on the Hadwiger number of circular arc graphs

  • Authors:

  • N. S. Narayanaswamy;N. Belkale;L. S. Chandran;N. Sivadasan

  • Affiliations:

  • Department of Computer Science and Engineering, Indian Institute of Technology, Chennai 600036, India;CSA Department, Indian Institute of Science, Bangalore 560012, India;CSA Department, Indian Institute of Science, Bangalore 560012, India;Strand Genomics, 237, Sir. C.V. Raman Avenue, Rajmahal Vilas, Bangalore 560080, India

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

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Abstract

The intention of this note is to motivate the researchers to study Hadwiger's conjecture for circular arc graphs. Let @h(G) denote the largest clique minor of a graph G, and let @g(G) denote its chromatic number. Hadwiger's conjecture states that @h(G)=@g(G) and is one of the most important and difficult open problems in graph theory. From the point of view of researchers who are sceptical of the validity of the conjecture, it is interesting to study the conjecture for graph classes where @h(G) is guaranteed not to grow too fast with respect to @g(G), since such classes of graphs are indeed a reasonable place to look for possible counterexamples. We show that in any circular arc graph G, @h(G)=