Geodesic
Distance perfectness of graphs
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 1, pp. 31-43

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In this paper, we propose a generalization of well known kinds of perfectness of graphs in terms of distances between vertices. We introduce generalizations of α-perfect, χ-perfect, strongly perfect graphs and we establish the relations between them. Moreover, we give sufficient conditions for graphs to be perfect in generalized sense. Other generalizations of perfectness are given in papers [3] and [7].
Keywords: perfect graphs, strongly perfect graphs, chromatic number 
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Włoch, Andrzej. Distance perfectness of graphs. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 1, pp. 31-43. http://geodesic.mathdoc.fr/item/DMGT_1999_19_1_a2/