# Thomas, Robin

## Does every subcubic triangle-free graph have fractional chromatic number at most 14/5? ★

Author(s): Heckman; Thomas

\begin{conjecture} Every triangle-free graph with maximum degree at most 3 has fractional chromatic number at most 14/5. \end{conjecture}

Keywords: fractional coloring

## Highly connected graphs with no K_n minor ★★★

Author(s): Thomas

\begin{problem} Is it true for all $n \ge 0$, that every sufficiently large $n$-\Def[connected]{connectivity (graph theory)} graph without a \Def[$K_n$]{complete graph} \Def[minor]{minor (graph theory)} has a set of $n-5$ vertices whose deletion results in a \Def{planar graph}? \end{problem}

Keywords: connectivity; minor