Degree conditions for Hamiltonian graphs to have [a,b] -factors containing a given Hamiltonian cycle

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Abstract

Let 1≤a<b be integers and G a Hamiltonian graph of order |G|≥(a+b)(2a+b)/b. Suppose that δ(G)≥a+2 and max{deg G(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.

Original languageEnglish
Pages (from-to)241-250
Number of pages10
JournalDiscrete Mathematics
Volume280
Issue number1-3
DOIs
Publication statusPublished - 2004 Apr 6
Externally publishedYes

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Keywords

  • Connected factor
  • Degree condition
  • Factor
  • Hamiltonian graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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