of the International Conference on Theory and Application of Mathematics and Informatics ICTAMI 2005 - Alba Iulia , Romania PERFECT TRANSVERSALS IN SOME GRAPH PRODUCTS
نویسندگان
چکیده
A perfect transversal of a graph is a set of vertices that meets any maximal clique, or any maximal stable set of the graph in exactly one vertex. In this paper we give some properties of perfect transversals in graph products. One of these properties is the characterization of the existence of perfect transversals in some graph products via perfect transversals of the factors. As an application we give a characterization of strongly perfectness of such graph products. We have also got similar results for the graph itself using graph decomposition. In order to obtain these results we have strongly used and we have given some new properties of graph homomorphisms and quasi-homomorphisms.
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