The q-perfect graphs
Let q be a positive integer. Many graphs admit a partial coloring with q colors and a clique partition such that each of the cliques is strongly colored, that is: contains the largest possible number of different colors. If a graph G and all its induced subgraphs have this property, we say that G is q-perfect (Lovasz). In a previous paper , the specific properties for the case q=2 were investigated. Here, we study some graphs which are q-perfect for other values of q, and more specially the balanced graphs.
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