-decompositions of some regular graphs
β Scribed by R.S. Manikandan; P. Paulraja
- Book ID
- 108113563
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 902 KB
- Volume
- 306
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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 Kotzig asked in 1979 what are necessary and sufficient conditions for a __d__βregular simple graph to admit a decomposition into paths of length __d__ for odd __d__>3. For cubic graphs, the existence of a 1βfactor is both necessary and sufficient. Even more, each 1βfactor is extendable
In this article, we show that every simple r-regular graph G admits a balanced P 4 -decomposition if r β‘ 0(mod 3) and G has no cut-edge when r is odd. We also show that a connected 4-regular graph G admits a P 4 -decomposition if and only if |E(G)| β‘ 0(mod 3) by characterizing graphs of maximum degr
A result on decompositions of regular graphs, Discrete Mathematics 105 (1992) 323-326. We prove that for any connected graph G and any integer r which is a common multiple of the degrees of the vertices in G, there exists a connected, r-regular, and G-decomposable graph H such that x(H) = x(G) and o