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All Outputs (92)

Line hypergraphs (1996)
Journal Article
Zverovich, V. E., Tyshkevich, R. I., Tyshkevich, R., & Zverovich, V. (1996). Line hypergraphs. Discrete Mathematics, 161(1-3), 265-283. https://doi.org/10.1016/0012-365X%2895%2900233-M

In this paper, we introduce a new multivalued function ℒ called the line hypergraph. The function ℒ generalizes two classical concepts at once, namely, of the line graph and the dual hypergraph. In terms of this function, proofs of some known theorem... Read More about Line hypergraphs.

Domination perfect graphs (1995)
Presentation / Conference
Zverovich, V. (1995, November). Domination perfect graphs. Presented at Computer Science Colloquium, Odense, Denmark

An induced subgraph characterization of domination perfect graphs (1995)
Journal Article
Zverovich, V. E., Zvervich, I. E., Zverovich, I., & Zverovich, V. (1995). An induced subgraph characterization of domination perfect graphs. Journal of Graph Theory, 20(3), 375-395. https://doi.org/10.1002/jgt.3190200313

Let γ(G) ι(G) be the domination number and independent domination number of a graph (G), respectively. A graph (G) is called domination perfect if γ(H) = ι(H), for every induced subgraph H of (G). There are many results giving a partial characterizat... Read More about An induced subgraph characterization of domination perfect graphs.

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.

Perfect graphs in domination theory (1992)
Presentation / Conference
Zverovich, V. (1992, June). Perfect graphs in domination theory. Presented at Seminar on Discrete Mathematics, Institute of Mathematics of the Academy of Science, Minsk, Belarus

The binding number of almost every graph (1991)
Presentation / Conference
Zverovich, V. (1991, June). The binding number of almost every graph. Presented at The 14th Conference on Discrete Mathematics of the South Science Centre of the AN USSR, Odessa, Ukraine

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.

Domination and independence in graphs (1990)
Presentation / Conference
Zverovich, V., & Zverovich, I. (1990, June). Domination and independence in graphs. Presented at The 3rd All-Union Seminar on Discrete Mathematics and Its Applications, Moscow, Russia