Rank decomposition under combinatorial constraints
β Scribed by Charles R. Johnson; Jeremy Miller
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 477 KB
- Volume
- 251
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __G__ = __(A, B; E)__ be a bipartite graph. Let __e__~1~, __e__~2~ be nonnegative integers, and __f__~1~, __f__~2~ nonnegative integerβvalued functions on __V(G)__ such that __e__~__i__~ β¦ |__E__| β¦ __e__~1~ + __e__~2~ and __f~i~(v)__ β¦ __d(v)__ β¦ __f__~1~__(v)__ + __f__~2~__(v)__ f
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.