Pairs of forbidden induced subgraphs for homogeneously traceable graphs

A graph GG is called homogeneously traceable if for every vertex vv of GG, GG contains a Hamilton path starting from vv. For a graph HH, we say that GG is HH-free if GG contains no induced subgraph isomorphic to HH. For a family HH of graphs, GG is called HH-free if GG is HH-free for every H∈HH∈H. Determining families of graphs HH such that every HH-free graph GG has some graph property has been a popular research topic for several decades, especially for Hamiltonian properties, and more recently for properties related to the existence of graph factors. In this paper we give a complete characterization of all pairs of connected graphs R,SR,S such that every 2-connected {R,S}{R,S}-free graph is homogeneously traceable.