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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 1less-than-or-equals, slanta<b be integers and G a Hamiltonian graph of order |G|greater-or-equal, slanted(a+b)(2a+b)/b. Suppose that δ(G)greater-or-equal, slanteda+2 and max{degG(x), degG(y)}greater-or-equal, slanteda|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
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