We review a characterization of domination perfect graphs in terms of forbidden induced subgraphs obtained by Zverovich and Zverovich [12] using a computer code. Then we apply it to a problem of unique domination in graphs recently proposed by Fischermann and Volkmann. 1 Domination perfect graphs Let G be a graph. A set D ⊆ V (G) is a dominating set of G if each vertex of G either belongs to D ...

In 2002, Aguilera et al. analyzed the performance of the disjunctive lift-and-project operator defined by Balas, Ceria and Cornuéjols on covering and packing polyhedra, in the context of blocking and antiblocking duality. Their results generalize Lovász’s Perfect Graph Theorem and a theorem of Lehman on ideal clutters. This study motivated many authors to work on the same ideas, providing alter...

We study a graph transformation (defined by Seidel) called switching which, given a graph G = ( V,E) and a subset W C Jf of its vertices, builds a new graph by exchanging the cocycle linking W to V\ W with its complement. Switching is an equivalence relation and the associated equivalence classes are called switching classes. A switching class is perfect if it contains only perfect graphs. We s...

A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. The b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph H of G. A graph is minimally b-impe...

A set D of vertices in a graph G = (V, E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdiv...

Korner [7] defined the notion of graph-entropy. He used it in [8] to simplify the proof of the Fredman-Komlos lower bound for the family size of perfect hash functions. We use this information theoretic notion to obtain a general method for formula size lower bounds. This method can be applied to low-complexity functions for which the other known general methods ([11, 12, 3] and see also [17] )...