Name
Abstract | ||
|---|---|---|
A simple, connected even graph G with vertex set V(G) and edge set E(G) is said to be ADCT (Arbitrarily Decomposable into Closed Trails) if for any collection of positive integers x 1, x 2,...,x m with $$\sum_{i=1}^m x_i = |E(G)|$$ and x i ≥ 3 for 1 ≤ i ≤ m, there exists a decomposition of G into closed trails (circuits) of lengths x 1, x 2,...,x m . In this note we construct an 8-regular ADCT graph on 6n vertices, for each each n ≥ 3. On the other hand, we also show that there are only finitely many 4-regular graphs which are ADCT. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s00373-008-0783-y | Graphs and Combinatorics |
Keywords | Field | DocType |
8-regular adct graph,positive integer,arbitrarily decomposable,4-regular graph,sparse graphs,m x_i,closed trails,graph decompositions.,graph g,arbitrary lengths,regular graph | Discrete mathematics,Topology,Combinatorics,Strongly regular graph,Vertex-transitive graph,Line graph,Graph power,Bound graph,Symmetric graph,Pathwidth,Mathematics,Complement graph | Journal |
Volume | Issue | ISSN |
24 | 3 | 1435-5914 |
Citations | PageRank | References |
1 | 0.45 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Elizabeth J. Billington | 1 | 109 | 27.90 |
| Nicholas J. Cavenagh | 2 | 92 | 20.89 |