## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# 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.

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996

Information for students and suggested topics for student talks