Cycles of given length in some \(K_{1,3}\)-free graphs (Q749554)

A graph G is \(K_{1,3}\)-free if no induced subgraph of G is isomorphic to \(K_{1,3}\). A graph G is pancyclic if it contains cycles of all possible lengths. The author proves that if any vertex cut of G contains a vertex v such that G(N(v)) is connected, then G is pancyclic. Further, if G(N(v)) is connected for any vertex v of G then the author proves that G is vertex pancyclic (i.e. each vertex of G is contained in cycles of all possible lengths). A polynomial time algorithm for constructing cycles of given length passing through a given vertex of G is given.