Circular chromatic number of triangle free graphs with given maximum average degree, extended abstract

In that paper we talk about triangle-free simple graphs with given maximum average degree less than 22/9. We give an upper bound for the circular chromatic number of such graphs which is at most 11/4. We give two other results whose proofs are omitted. We use a discharging method with forbidden configurations. We also omit in this paper the proof that they are indeed forbidden. These proofs rely on a recent paper [A. Raspaud, X. Zhu, List circular coloring of trees and cycles, (2006)] of Raspaud and Zhu and are all straight-forward.