Self-complementary graphs and Ramsey numbers Part I: the decomposition and construction of self-complementary graphs

Self-complementary circulant graphs

The properties of self-complementary graphs and new lower bounds for diagonal Ramsey numbers

Some properties of self-complementary graphs have been studied and 3 new lower bounds for diagonal Ramsey numbers have been obtained. They are: R(17, 17) ≥ 8917, R(18, 18) ≥ 11005, R(19, 19) ≥ 17885.

Self-Complementary Vertex-Transitive Graphs

A graph Γ is self-complementary if its complement is isomorphic to the graph itself. An isomorphism that maps Γ to its complement Γ is called a complementing isomorphism. The majority of this dissertation is intended to present my research results on the study of self-complementary vertex-transitive graphs. I will provide an introductory mini-course for the backgrounds, and then discuss four pr...

Homogeneously almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to the graph obtained from its complement by removing a 1-factor. In this paper, we study a special class of vertex-transitive almost self-complementary graphs called homogeneously almost selfcomplementary. These graphs occur as factors of symmetric index-2 homogeneous factorizations of the “cocktail party graphs” K2n − nK2. We con...

On almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to one of its almost complements Xc − I, where Xc denotes the complement of X and I a perfect matching (1-factor) in Xc. Almost self-complementary circulant graphs were first studied by Dobson and Šajna in 2004. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In par...