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Rank decomposition under combinatorial constraints

✍ Scribed by Charles R. Johnson; Jeremy Miller


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
477 KB
Volume
251
Category
Article
ISSN
0024-3795

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✍ H. J. Broersma; R. J. Faudree; J. Den Van Heuvel; H. J. Veldman πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 339 KB

## Abstract Let __G__ = __(A, B; E)__ be a bipartite graph. Let __e__~1~, __e__~2~ be nonnegative integers, and __f__~1~, __f__~2~ nonnegative integer‐valued functions on __V(G)__ such that __e__~__i__~ ≦ |__E__| ≦ __e__~1~ + __e__~2~ and __f~i~(v)__ ≦ __d(v)__ ≦ __f__~1~__(v)__ + __f__~2~__(v)__ f

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We prove that if s and t are positive integers and if G is a triangle-free graph with minimum degree s + t, then the vertex set of G has a decomposition into two sets which induce subgraphs of minimum degree at least s and t, respectively.