Forbidden pairs of disconnected graphs for traceability in connected graphs

Abstract

Let H be a class of given graphs. A graph G is said to be H-free if G contains no induced copies of H for every H?H. A graph is called traceable if it contains a Hamilton path. Faudree and Gould (1997) characterized all the pairs {R,S} of connected subgraphs such that every connected {R,S}-free graph is traceable. Li and Vrána (2016) first consider the disconnected forbidden subgraphs, and characterized all pairs of disconnected forbidden subgraphs for hamiltonicity. In this article, we characterize all pairs {R,S} of graphs such that there exists an integer n0 such that every connected {R,S}-free graph of order at least n0 is traceable.