Claw-free circular-perfect graphs

The circular chromatic number of a graph is a well-studied refinement of the chromatic number. Circular-perfect graphs is a superclass of perfect graphs defined by means of this more general coloring concept. This paper studies claw-free circular-perfect graphs. A consequence of the strong perfect graph theorem is that minimal circular-imperfect graphs G have min{α(G), ω(G)} = 2. In contrast to this result, it is shown in [9] that minimal circular-imperfect graphs G can have arbitrarily large independence number and arbitrarily large clique number. We prove that claw-free minimal circular-imperfect graphs G have min{α(G), ω(G)} ≤ 3.

• Type: Journal
• Year: 2007
• Where: ENDM
• Authors: Arnaud Pêcher, Xuding Zhu
• Keywords: Chromatic Number, Circular Chromatic Number, ENDM 2007, Minimal Circular-imperfect Graphs