On the odd cycles of normal graphs Original Research Article

A graph is normal if there exists a cross-intersecting pair of set families one of which consists of cliques while the other one consists of stable sets, and furthermore every vertex is obtained as one of these intersections. It is known that perfect graphs are normal while C5, C7, andC̄7 are not. We conjecture that these three graphs are the only minimally not normal graphs. We give sufficient conditions for a graph to be normal and we characterize those normal graphs that are triangle-free.