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,
Multicolored forests in bipartite decompositions of graphs
β Scribed by Noga Alon; Richard A Brualdi; Bryan L Shader
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 322 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Truszczydski, M., Decompositions of graphs into forests with bounded maximum degree, Discrete Mathematics 98 (1991) 207-222.
We construct decompositions of L(K,,), M(K,,) and T(K,,) into the minimum number of line-disjoint spanning forests by applying the usual criterion for a graph to be eulerian. This gives a realization of the arboricity of each of these three graphs. ## 1. Preliminaries In this paper a graph is cons
## 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
## 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.