Abstract
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 ) ⩾ χ ( 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 ) ⩽ 2 χ ( G ) − 1 , and there is a family with equality. So, it makes sense to study Hadwiger's conjecture for this family.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
