Pairs of forbidden induced subgraphs for homogeneously traceable graphs

A graph G is called homogeneously traceable if for every vertex v of G , G contains a Hamilton path starting from v . For a graph H , we say that G is H -free if G contains no induced subgraph isomorphic to H . For a family H of graphs, G is called H -free if G is H -free for every H ∈ H . Determining families of graphs H such that every H -free graph G 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 , S such that every 2-connected { R , S } -free graph is homogeneously traceable.