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All Outputs (31)

Disproof of a Conjecture in the Domination Theory (1994)
Journal Article
Zverovich, V. E., Zverovich, I. E., Zverovich, I., & Zverovich, V. (1994). Disproof of a Conjecture in the Domination Theory. Graphs and Combinatorics, 10(2), 389-396. https://doi.org/10.1007/BF02986690

In [1] C. Barefoot, F. Harary and K. Jones conjectured that for cubic graphs with connectivity three the difference between the domination and independent domination numbers is at most one. We disprove this conjecture and give an exhaustive answer to... Read More about Disproof of a Conjecture in the Domination Theory.

Contributions to the theory of graphic sequences (1992)
Journal Article
Zverovich, V. E., Zverovich, I. E., Zverovich, I., & Zverovich, V. (1992). Contributions to the theory of graphic sequences. Discrete Mathematics, 105(1-3), 293-303. https://doi.org/10.1016/0012-365X%2892%2990152-6

In this article we present a new version of the Erdős-Gallai theorem concerning graphicness of the degree sequences. The best conditions of all known on the reduction of the number of Erdős-Gallai inequalities are given. Moreover, we... Read More about Contributions to the theory of graphic sequences.

A characterization of domination perfect graphs (1991)
Journal Article
Zverovich, V. E., Zverovich, I. E., Zverovich, I., & Zverovich, V. (1991). A characterization of domination perfect graphs. Journal of Graph Theory, 15(2), 109-114. https://doi.org/10.1002/jgt.3190150202

Let γ(G) and i(G) be the domination number and independent domination number of a graph G, respectively. Sumner and Moore [8] define a graph G to be domination perfect if γ(H) = i(H), for every induced subgraph H of G. In this article, we give a fini... Read More about A characterization of domination perfect graphs.