3 problems

For a positive integer $k$, let $f(k)$ be the maximum possible chromatic number of a graph whose edge set can be partitioned into at most $k$ complete bipartite graphs, and set…

Let $G=(V,E)$ be a graph, and let $\tau(G)$ denote the minimum number of pairwise edge-disjoint complete bipartite subgraphs of $G$ whose edges partition $E$. Let $\beta(G)$ denote…

Let $G=(V,E)$ be a graph, and let $\tau(G)$ denote the minimum number of pairwise edge-disjoint complete bipartite subgraphs of $G$ whose edges partition $E$. Let $\alpha(G)$ be th…