On canonical decomposition of bipartite graphs
β Scribed by J.M. Vanherpe
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 91 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1571-0653
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In this paper we discuss isomorphic decompositions of regular bipartite graphs into trees and forests. We prove that: (1) there is a wide class of r-regular bipartite graphs that are decomposable into any tree of size r, (2) every r-regular bipartite graph decomposes into any double star of size r,
## Abstract A short proof is given of the impossibility of decomposing the complete graph on __n__ vertices into __n__β2 or fewer complete bipartite graphs.
## 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