Degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle |
| |
Authors: | Haruhide Matsuda |
| |
Institution: | Department of General Education, Kyushu Tokai University, Choyo, Aso, Kumamoto 869-1404, Japan |
| |
Abstract: | Let 1a<b be integers and G a Hamiltonian graph of order |G|(a+b)(2a+b)/b. Suppose that δ(G)a+2 and max{degG(x), degG(y)}a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G. Then G has an a,b]-factor which is edge-disjoint from a given Hamiltonian cycle. The lower bound on the degree condition is sharp. For the case of odd a=b, there exists a graph satisfying the conditions of the theorem but having no desired factor. As consequences, we have the degree conditions for Hamiltonian graphs to have a,b]-factors containing a given Hamiltonian cycle. |
| |
Keywords: | Author Keywords: Factor Connected factor Degree condition Hamiltonian graph |
本文献已被 ScienceDirect 等数据库收录! |
|