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In this paper we characterize all triples of connected graphs C,X,Y (where C is a claw) and such that every 2-connected CXY-free graph G is hamiltonian. This result together with a previous result by Faudree, Gould, Jacobson, and Lesniak give a full characterization of triples of forbidden subgraphs implying hamiltonicity of 2-connected 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...
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