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Preprints, Working Papers, ... Year : 2012

Reed's conjecture on some special classes of graphs

Abstract

Reed conjectured that for any graph $G$, $\chi(G) \leq \lceil \frac{\omega(G)+\Delta(G)+1}{2}\rceil$, where $\chi(G)$, $\omega(G)$, and $\Delta(G)$ respectively denote the chromatic number, the clique number and the maximum degree of $G$. In this paper, we verify this conjecture for some special classes of graphs, in particular for subclasses of $P_5$-free graphs or $Chair$-free graphs.
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Dates and versions

hal-00694158 , version 1 (03-05-2012)
hal-00694158 , version 2 (29-10-2012)

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Jean-Luc Fouquet, Jean-Marie Vanherpe. Reed's conjecture on some special classes of graphs. 2012. ⟨hal-00694158v1⟩
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