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The pseudoachromatic index of a graph is the maximum number of colors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color, then this maximum is known as achromatic index. Both indices have been widely studied. A geometric graph is a graph drawn… (More)
A graph G is trivially perfect if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) α(G) equals the number of (maximal) cliques m(G). We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.