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.
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.
