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Sufficient conditions for graphs to have (g, f)-factors

✍ Scribed by Yoshimi Egawa; Mikio Kano

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
170 KB
Volume
151
Category
Article
ISSN
0012-365X

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✦ Synopsis

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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Let G be a graph with vertex set V and let g, f : V Γ„ Z + . We say that G has all ( g, f )-factors if G has an h-factor for every h: V Γ„ Z + such that g(v) h(v) f (v) for every v # V and at least one such h exists. In this note, we derive from Tutte's f-factor theorem a similar characterization for