Optional decompositions under constraints
✍ Scribed by H. Föllmer; D. Kramkov
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 505 KB
- Volume
- 109
- Category
- Article
- ISSN
- 1432-2064
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📜 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 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
## Abstract We show that the vertex set of any graph __G__ with __p__⩾2 vertices can be partitioned into non‐empty sets __V__~1~, __V__~2~, such that the maximum degree of the induced subgraph 〈__V__~i~〉 does not exceed where p^i^ = |__V__^i^|, for __i__=1, 2. Furthermore, the structure of the in