Forbidden set of induced subgraphs for [formula omitted]-connected supereulerian graphs

Abstract

Let H={H1,…,Hk} be a set of connected graphs. A graph is said to be H-free if it does not contain any member of H as an induced subgraph. We show that if the following statements hold, •|H|≥2,•K1,3∈H,•for any integer n0, every 2-connected H-free graph G of order at least n0 is supereulerian, i.e.,G has a spanning closed trail,then H∖{K1,3} contains an Ni,j,k or a path where Ni,j,k denotes the graph obtained by attaching three vertex-disjoint paths of lengths i,j,k≥0 to a triangle.As an application, we characterize all the forbidden triples H with K1,3∈H such that every 2-connected H-free graph is supereulerian. As a byproduct, we also characterize minimal 2-connected non-supereulerian claw-free graphs.