A partition of the edge set of a graph H into subsets inducing graphs H,, . . . , H, isomorphic to a graph G is said to be a G-decomposition of H. A G-decomposition of H is resolvable if the set {H,, . . . , H,} can be partitioned into subsets, called resolution classes, such that each vertex of H
A note on the tree decompositions of graphs
β Scribed by Shi Minyong
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 288 KB
- Volume
- 42
- Category
- Article
- ISSN
- 1001-6538
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For a graph G, if E(G) can be partitioned into several pairwise disjoint sets as {EI,& . . . , El} such that for any i with 1 *3. We prove that (i) for any %-graph of order n 23, it has both a {n,n -2}tree-decomposition and a {n -1,n -1}-tree-decomposition, and moreover, these two kinds of tree-deco
## Abstract In the study of decompositions of graphs into paths and cycles, the following questions have arisen: Is it true that every graph __G__ has a smallest path (resp. pathβcycle) decomposition __P__ such that every odd vertex of __G__ is the endpoint of exactly one path of __P__? This note g
with β¦ G G V r2 q 10 h V log V , and h y 1 divides E , then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.