We generalize the concept of perfect graphs in terms of additivity of a functional called graph entropy. The latter is an information theoretic functional on a graphG with a probability distributionP on its vertex set. For any fixedP it is sub-additive with respect to graph union. The entropy of the complete graph equals the sum of those ofG and its complement G iffG is perfect. We generalize this recent result to characterize all the cases when the sub-additivity of graph entropy holds with equality.
AMS subject classification code (1991)05 C 75 94 A 17 05 C 15 94 A 15
Unable to display preview. Download preview PDF.
- K. Cameron, J. Edmonds: Lambda composition, preprint.Google Scholar
- D. Kelly: Comparability graphs, in: “Graphs and Orders” (I. Rival, ed.), D. Reidel Publ. Co. (1985), 3–40.Google Scholar
- J. Körner: Coding of an information source having ambiguous alphabet and the entropy of graphs, in: “Transactions of the 6th Prague Conference on Information Theory, etc.”, Academia, Prague, (1973), 411–425.Google Scholar
- L. Lovász: Perfect graphs, in: “Selected Topics in Graph Theory” Vol.2 (I. W. Beineke, R. J. Wilson, Eds.), Academic Press, New York-London (1983), 55–87.Google Scholar