6 problems

For a graph $G$, write $chi^*(G)$ for its fractional chromatic number and $\operatorname{oddgirth}(G)$ for the length of its shortest odd cycle; a t-minor is the graph-minor operat…

Fractional packing conjectures. There exists a constant $C>0$ such that, for every graph $G$,

Kelly and Postle's conjecture. Every triangle-free graph admits a probability distribution on independent sets such that, for every vertex $v$,

Star-dichromatic conjecture.

Let $k$ be a positive integer. A graph $H$ of odd-girth $2k+1$ bounds a class of graphs if every graph in that class admits a graph homomorphism to $H$. Consider the class of $K_4$…

Clique-local fractional Reed conjecture. Every graph $G$ satisfies