Degree conditions for Hamiltonian graphs to have [a,b]-factors containing a given Hamiltonian cycle
نویسندگان
چکیده
منابع مشابه
Degree conditions for the existence of [k, k+1]-factors containing a given Hamiltonian cycle
Let k ≥ 2 be an integer and G a 2-connected graph of order |G| ≥ 3 with minimum degree at least k. Suppose that |G| ≥ 8k − 16 for even |G| and |G| ≥ 6k − 13 for odd |G|. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{degG(x), degG(y)} ≥ |G|/2 for each pair of nonadjacent vertices x and y in G. This is best possible in the sense that there exists a graph havi...
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We prove the following best possible result. Let k ≥ 2 be an integer and G be a graph of order n with minimum degree at least k. Assume n ≥ 8k− 16 for even n and n ≥ 6k−13 for odd n. If the degree sum of each pair of nonadjacent vertices of G is at least n, then for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. Submitted: December 15, 1997; Accepted: November 27, 1...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2003.10.015