All Outputs (3)

Upper domination and upper irredundance perfect graphs (1998)
Journal Article
Gutin, G., & Zverovich, V. (1998). Upper domination and upper irredundance perfect graphs. Discrete Mathematics, 190(1-3), 95-105. https://doi.org/10.1016/S0012-365X%2898%2900036-3

Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. A graph G is called IR-perfect if Γ(H)... Read More about Upper domination and upper irredundance perfect graphs.

Line hypergraphs: A survey (1998)
Journal Article
Tyshkevich, R., & Zverovich, V. (1998). Line hypergraphs: A survey. Acta Applicandae Mathematicae, 52(1), 209-222. https://doi.org/10.1023/A%3A1005963110362

The survey is devoted to line graphs and a new multivalued function L called the line hypergraph. This function generalizes two classical concepts at once, namely the line graph and the dual hypergraph. In a certain sense, line graphs and dual hyperg... Read More about Line hypergraphs: A survey.

The Ratio of the Irredundance Number and the Domination Number for Block-Cactus Graphs (1998)
Journal Article
Zverovich, V. (1998). The Ratio of the Irredundance Number and the Domination Number for Block-Cactus Graphs. Journal of Graph Theory, 29(3), 139-149. https://doi.org/10.1002/%28SICI%291097-0118%28199811%2929%3A3%3C139%3A%3AAID-JGT2%3E3.0.CO%3B2-R

Let γ(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [Proc. 9th Southeast Conf. on Combin., Graph Theory & Comp. (1978) 43-56] and Bollobás and Cockayne [J. Graph Theory (1979) 241-2... Read More about The Ratio of the Irredundance Number and the Domination Number for Block-Cactus Graphs.