4 problems

Maffray–Thomas conjecture. Every bipartisan graph is a quasi-parity graph.

Let $G$ be a Berge graph, that is, a graph with no odd hole and no odd antihole. Let $\overline{G}$ denote its complement, let a 2-join be the decomposition defined earlier in the…

Even-pair or odd-pair conjecture. For every Berge graph $G$ on at least two vertices, either $G$ or $\overline{G}$ has an even pair, or $G$ or $\overline{G}$ has an odd pair of cli…

Let $G$ be a Berge graph with more than one vertex, and let $\overline{G}$ be its complement. A friend pair and a pair of enemy cliques are the structures defined in the source. Bu…