Extremal number of theta graphs of order 7

Abstract

For a set of graphsF, letH(n;F) denote the class of non-bipartiteHamiltonian graphs onnvertices that does not contain any graph ofFas a subgraphandh(n;F) = max{E(G) :G∈H(n;F)}whereE(G) is the number of edges inG.In this paper we determineh(n;{θ4, θ5, θ7}) andh(n;θ7) for sufficiently odd largen. Our result confirms the conjecture made in [1] fork= 3.