Decompositions of homology manifolds and their graphs
β Scribed by David Barnette
- Book ID
- 112889015
- Publisher
- The Hebrew University Magnes Press
- Year
- 1982
- Tongue
- English
- Weight
- 427 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0021-2172
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π SIMILAR VOLUMES
## Abstract An island decomposition of a graph __G__ consists of a set of vertexβdisjoint paths which cover the vertex set of __G.__ If the endpoints of the paths are mutually nonadjacent, then we have an atoll decomposition. We characterize graphs requiring two paths in an island decomposition yet
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