Circular chromatic number of triangle free graphs with given maximum average degree, extended abstract. Andr´ e Raspaud LaBRI Universit´ e Bordeaux I, Talence, France raspaud@labri.fr Nicolas Roussel 1 National Sun Yat-Sen University Kaohsiung, Taiwan roussel@labri.fr 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 [4] of Raspaud and Zhu and are all straight-forward. 1 Partially supported by EGIDE, programme Lavoisier Electronic Notes in Discrete Mathematics 28 (2007) 507–514 1571-0653/$ – see front matter © 2007 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.01.078