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A characterization of a graph which has a 2-factor

✍ Scribed by Y. Abe


Book ID
104349080
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
234 KB
Volume
13
Category
Article
ISSN
0893-9659

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Domination in a graph with a 2-factor
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## Abstract Let Ξ³(__G__) be the domination number of a graph __G__. Reed 6 proved that every graph __G__ of minimum degree at least three satisfies Ξ³(__G__) ≀ (3/8)|__G__|, and conjectured that a better upper bound can be obtained for cubic graphs. In this paper, we prove that a 2‐edge‐connected cu

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In this article, we consider the following problem: Given a bipartite graph G and a positive integer k, when does G have a 2-factor with exactly k components? We will prove that if , then, for any bipartite graph H = (U 1 , U 2 ; F ) with |U 1 | ≀ n, |U 2 | ≀ n and βˆ†(H) ≀ 2, G contains a subgraph i

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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