A better lower bound on average degree of k-list-critical graphs

Abstract

We improve the best known bounds on average degree of $k$-list-critical graphs for $k\ge 6$. Specifically, for $k\ge 7$ we show that every non-complete $k$-list-critical graph has average degree at least $k-1+\frac{(k-3{)}^2(2k-3)}{k^4-2k^3-11k^2+28k-14}$ and every non-complete $6$-list-critical graph has average degree at least $5+\frac{93}{766}$. The same bounds hold for online $k$-list-critical graphs.