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Reports (Research Report) Year : 2007

Circular Choosability


In this paper, we study the notion of circular choosability recently introduced by Mohar and Zhu. First, we provide a negative answer to a question of Zhu about circular cliques. We next prove that, for every graph G, cch(G) = O( ch(G) + ln |V(G)| ). We investigate a generalisation of circular choosability, circular f-choosability, when f is a function of the degrees. We also consider the circular choice number of planar graphs. Mohar asked for the value of tau := sup{ cch(G) : G is planar }, and we prove that 6 <= tau <= 8, thereby providing a negative answer to another question of Mohar. Finally, we study the circular choice number of planar and outerplanar graphs with prescribed girth, and graphs with bounded density.
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Dates and versions

inria-00086981 , version 1 (20-07-2006)
inria-00086981 , version 2 (01-08-2006)


  • HAL Id : inria-00086981 , version 2


Frédéric Havet, Ross Kang, Tobias Müller, Jean-Sébastien Sereni. Circular Choosability. [Research Report] RR-5957, INRIA. 2007, pp.33. ⟨inria-00086981v2⟩
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