Narayanaswamy, NS and Belkale, N and Chandran, LS and Sivadasan, N (2007) A note on the Hadwiger number of circular arc graphs. In: Information Processing Letters, 104 (1). pp. 10-13.
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The intention of this note is to motivate the researchers to study Hadwiger's conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G, and let χ(G) denote its chromatic number. Hadwiger's conjecture states that η(G)greater-or-equal, slantedχ(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 η(G) is guaranteed not to grow too fast with respect to χ(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, η(G)less-than-or-equals, slant2χ(G)−1, and there is a family with equality. So, it makes sense to study Hadwiger's conjecture for this family.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Department/Centre:||Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)|
|Date Deposited:||05 Mar 2010 08:17|
|Last Modified:||19 Sep 2010 05:56|
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