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Sufficient conditions for a graph to have factors

✍ Scribed by Mikio Kano

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
457 KB
Volume
80
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

Sufficient conditions for graphs to have
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We give sufficient conditions for a graph to have a (g,f)-factor. For example, we prove that a graph G has a (g,f)-factor if g(v) < f(v) for all vertices v of G and g(x)/deg~(x) <~ f(y)/deg~(y) for all adjacent vertices x and y of G.

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## Abstract Ore derived a sufficient condition for a graph to contain a Hamiltonian cycle. We obtain a sufficient condition, similar to Ore's condition, for a graph to contain a Hamiltonian cycle and a 1‐factor which are edge disjoint.

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✍ Li, Yanjun; Mao-cheng, Cai πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 131 KB πŸ‘ 2 views

Let G be a graph of order n, and let a and b be integers such that a+b for any two nonadjacent vertices u and v in G. This result is best possible, and it is an extension of T. Iida and T. Nishimura's results (T. Iida and T. Nishimura, An Ore-type condition for the existence of k-factors in graphs,