In my studies of graph theory I recently came across the following interesting question that got me stuck, but first a definition:
A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph.
The question involved here is:
Let G be a finite and simple undirected graph which is perfect (all subgraphs of it are perfect) and we are asked to prove G contains no odd cycle of length greater than three
To be quite honest, I cannot seem to relate the lack of odd cycles to the graph being perfect, so I have no idea on this here and I would certainly appreciate help on this.