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

Research output: Contribution to journalArticle

11 Citations (Scopus)

### 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 language English 241-250 10 Discrete Mathematics 280 1-3 https://doi.org/10.1016/j.disc.2003.10.015 Published - 2004 Apr 6 Yes

Hamiltonians

### Keywords

• Connected factor
• Degree condition
• Factor
• Hamiltonian graph

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

In: Discrete Mathematics, Vol. 280, No. 1-3, 06.04.2004, p. 241-250.

Research output: Contribution to journalArticle

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