# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, September 23, 2014, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Jan Volec

## Subcubic triangle-free graphs have fractional chromatic number at most 14/5

A fractional coloring of a graph $G$ is an assignment of non-negative weights to every independent set of $G$ in such a way that for every vertex $v$ of $G$, the sum of the weights of the independent sets containing $v$ is at least one. The weight of a fractional coloring is the total sum of the weights over all independent sets, and the fractional chromatic number is the smallest number $k$ such that there exists a fractional coloring of the weight $k$. In this talk, we show that every triangle-free graph with maximum degree 3 has fractional chromatic number at most $14/5$, thus confirming a conjecture of Heckman and Thomas.

This is joint work with Zdenek Dvorak and Jean-Sebastien Sereni.

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