论文信息 - Fan-Type Conditions for Collapsible Graphs

Fan-Type Conditions for Collapsible Graphs

A graph G is collapsible if for every even subset R <;; V ( G), there is a spanning connected subgraph of G whose set of odd degree vertices is R. A graph is supereulerian if it contains a spanning closed trail. It is known that every collapsible graph is supereulerian. A graph G of order n is said to satisfy a Fan type condition if max{d(u),d(v)} 2: n/(g 2)p E for each pair of vertices u, v at distance two1 where g E {3, 4} is the girth of G, and p 2: 2 and , 2: 0 are fixed numbers. In this paper, we study the Fan-type conditions for collapsible graphs and supereulerian graphs.

Zhi-Hong Chen

[1] Hong-Jian Lai,et al. Supereulerian Graphs and the Petersen Graph , 1996, J. Comb. Theory, Ser. B.

[2] Paul A. Catlin,et al. Supereulerian graphs: A survey , 1992, J. Graph Theory.

[3] Hong-Jian Lai,et al. Collapsible graphs and matchings , 1993, J. Graph Theory.

[4] Paul A. Catlin,et al. A reduction method to find spanning Eulerian subgraphs , 1988, J. Graph Theory.

[5] Paul A. Catlin. Contractions of graphs with no spanning eulerian subgraphs , 1988, Comb..

[6] Henk Jan Veldman. On dominating and spanning circuits in graphs , 1994, Discret. Math..

[7] Ronald J. Gould,et al. Updating the hamiltonian problem - A survey , 1991, J. Graph Theory.

[8] J. E. Williamson,et al. On Spanning and Dominating Circuits in Graphs , 1977, Canadian Mathematical Bulletin.

[9] Zhi-Hong Chen. A degree condition for spanning eulerian subgraphs , 1993, J. Graph Theory.

[10] Zhi-Hong Chen. Spanning closed trails in graphs , 1993, Discret. Math..

[11] Henk Jan Veldman,et al. On circuits and pancyclic line graphs , 1986, J. Graph Theory.

[12] Hong-Jian Lai. Eulerian subgraphs containing given vertices and hamiltonian line graphs , 1998, Discret. Math..

[13] F. Harary,et al. On Eulerian and Hamiltonian Graphs and Line Graphs , 1965, Canadian Mathematical Bulletin.