Forbidden subgraphs and the existence of paths and cycles passing through specified vertices

In [2], Duffus et al. showed that every connected graph G which contains no induced subgraph isomorphic to a claw or a net is traceable. And they also showed that if a 2-connected graph G satisfies the above conditions, then G is hamiltonian. In this paper, modifying the conditions of Duffus et al.'s theorems, we give forbidden structures for a specified set of vertices which assures the existence of paths and cycles passing through these vertices.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Jun Fujisawa, Katsuhiro Ota, Takeshi Sugiyama, Masao Tsugaki
• Keywords: 2-connected Graph, Connected Graph, DM 2008, Duffus Et Al