Extremal number of theta graphs of order 7

Abstract

For a set of graphs F , let H(n; F ) denote the class of non-bipartite Hamiltonian graphs on n vertices that does not contain any graph of F as a subgraph and h(n; F ) = max{E (G) : G E H(n; F )} where E (G) is the number of edges in G. In this paper we determine h(n; {84, 85, 87}) and h(n; 87) for sufficiently odd large n. Our result confirms the conjecture made in [7] for k = 3.