A decomposition theory of graph degree sequences is elaborated. The graphs that can be uniquely determined by their degree sequences are classified. A number of results on characterizations, enumerations, and algorithmic recognizability conditions for special classes of graphs is obtained (some of them jointly with former and current Ph.D.students), a number of classical problems is solved for these classes. In recent years a general graph decomposition theory and a theory of representing graphs as the values of the function "Line graph" are being developed.
Biography
Graduated from the Physics and Mathematics Department of the Belarus State University in 1952 (the Higher Algebra Chair). Ph.D., 1959, the Belarus State University. Doct. Sci., 1984, the Glushkov Institute of Cybernetics, the National Academy of Sciences of Ukraine. 100 publications.
Distinguished Educational Worker of Republic of Belarus (1992), State Prize of Republic of Belarus (1998). A member of the Belarus Mathematical Society and the Belarus Operation Research Society.
Main publications:
Suprunenko D. A., Tyshkevich R. I. Commutative matrices. "Academic press", New York, 1968.
Emelichev V. A., Melnikov O. I., Servanov V. I., Tyshkevich R. I. Lectures on graph theory. B. I. Wissenschaftsverlag, Mannheim/Leipzig/Wein/Zurich. 1994, 317 p.
Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Yemelichev V. A., and Zverovich I. E. Exercises in graph theory. Kluwer Texts in Math. Sci. 19. Dordrecht: Kluwer Acad. Publ. 1998, 354 p.
Tyshkevich R. I. and Zverovich I. E. Line hypergraphs — a survey // Acta applicandae mathematicae 1998, 52 (1/3), 209–222.
Tyshkevich R. I. Decomposition theorem and unigraphs // Discrete Math. 2000, 220, (1–3), 201–238.
O. V. Maksimovich, R. I. Tyshkevich, “Hamiltonian completion”, Tr. Inst. Mat., 19:2 (2011), 87–90
2010
2.
R. I. Tyshkevich, P. V. Skums, S. V. Suzdal', “Algebraic graph decomposition theory”, Tr. Inst. Mat., 18:1 (2010), 99–115
3.
O. V. Maksimovich, R. I. Tyshkevich, “Injective $L(2,1)$-coloring of split indecomposable unigraphs”, Tr. Inst. Mat., 18:1 (2010), 79–91
2009
4.
P. V. Skums, R. I. Tyshkevich, “Reconstruction conjecture for graphs with restrictions for 4-vertex paths”, Diskretn. Anal. Issled. Oper., 16:4 (2009), 87–96
O. V. Maksimovich, R. I. Tyshkevich, “Injective $L(2,1)$-coloring as an optimization problem on the set of permutations of graph vertices: domishold graphs”, Tr. Inst. Mat., 17:1 (2009), 110–118
A. J. Perez Tchernov, R. I. Tyshkevich, “On the recognition algorithm of edge intersection graphs of linear $3$-uniform hypergraphs: prelarge cliques”, Tr. Inst. Mat., 15:2 (2007), 78–89
1993
7.
A. G. Levin, R. I. Tyshkevich, “Edge hypergraphs”, Diskr. Mat., 5:1 (1993), 112–129; Discrete Math. Appl., 3:4 (1993), 407–427
V. È. Zverovich, I. É. Zverovich, R. I. Tyshkevich, “Graphs with a matroid number that does not exceed 2”, Diskr. Mat., 2:2 (1990), 82–88
9.
R. I. Tyshkevich, A. A. Chernyak, “Yet another method of enumerating unmarked combinatorial objects”, Mat. Zametki, 48:6 (1990), 98–105; Math. Notes, 48:6 (1990), 1239–1245
R. I. Tyshkevich, “Pronormal regular subgroups of the finite symmetric group”, Zap. Nauchn. Sem. LOMI, 103 (1980), 132–139; J. Soviet Math., 24:4 (1984), 470–475
R. I. Tyshkevich, “Relations admitting a transitive group of automorphisms”, Mat. Sb. (N.S.), 97(139):2(6) (1975), 262–277; Math. USSR-Sb., 26:2 (1975), 245–259
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