Even-Pair Skew-Partition

An even-pair skew-partition is a partition of the vertex set of a graph $G$ into four sets $A,B,C,D$ s.t. $A$ is complete to $B$ and $C$ is anti-complete to $D$, and any two non-adjacent vertices in $A$ or $B$ are an even pair.

Question 1 Is it true that every Berge graph is either basic or has a $2$-join or has an even-pair skew-partition?

Question 2 Is even-pair skew-partition a composition?

Contributed by Bruce Reed

Back to the main index for Perfect Graphs.