3 problems

For each positive integer $k$, let $\alpha_k$ be the minimum value such that there is a constant $c_k$ with … whenever $G$ is $k$-degenerate and has maximum degree at most $D$. Let…

Let $G$ be a graph with maximum degree $Delta(G)=4$ and maximum average degree $\operatorname{mad}(G)<4$. The maximum-average-degree conjecture. asserts … Here $chi^2(G)$ is the 2-…

Maximum-average-degree partition conjecture. If