Forbidden triples for Hamiltonicity
If \(X\), \(Y\), \(Z\) are graphs, we say that a graph \(G\) is \(XYZ\)-free if \(G\) does not contain \(X\), \(Y\) or \(Z\) as an induced subgraph. The author characterizes all triples of connected graphs \(C\), \(X\), \(Y\), where \(C\) is the claw \(K_{1,3}\), such that every \(2\)-connected \(CXY\)-free graph is Hamiltonian. This result together with a previous result of Faudree, Gould, Jacobson and Lesniak gives a complete characterization of triples of forbidden subgraphs implying Hamiltonicity of \(2\)-connected graphs.
scientific article; zbMATH DE number 1792399