Pairs of forbidden induced subgraphs for homogeneously traceable graphs

Binlong Li, Binlong Li, Haitze J. Broersma, Shenggui Zhang

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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.
Original languageEnglish
Pages (from-to)2800-2818
Number of pages19
JournalDiscrete mathematics
Issue number18
Publication statusPublished - Sep 2012


  • MSC-05C
  • Induced subgraph
  • Forbidden subgraph
  • Homogeneously traceable graph
  • Hamiltonian graph


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