Name
Abstract | ||
|---|---|---|
A resolvable (balanced) path design, RBPD(v, k, λ) is the decomposition of λ copies of the complete graph on v vertices into edge-disjoint subgraphs such that each subgraph consists of vk vertex-disjoint paths of length k − 1 (k vertices). It is shown that an RBPD(v, 3, λ) exists if and only if v ≡ 9 (modulo 12/gcd(4, λ)). Moreover, the RBPD(v, 3, λ) can have an automorphism of order v3. For k > 3, it is shown that if v is large enough, then an RBPD(v, k, 1) exists if and only if v ≡ k2 (modulo lcm(2k − 2, k)). Also, it is shown that the categorical product of a k-factorable graph and a regular graph is also k-factorable. These results are stronger than two conjectures of P. Hell and A. Rosa |
Year | DOI | Venue |
|---|---|---|
1985 | 10.1016/0097-3165(85)90033-0 | Journal of Combinatorial Theory, Series A |
Field | DocType | Volume |
Discrete mathematics,Graph,Complete graph,Combinatorics,Vertex (geometry),Modulo,Categorical variable,Automorphism,Regular graph,If and only if,Mathematics | Journal | 39 |
Issue | ISSN | Citations |
2 | 0097-3165 | 11 |
PageRank | References | Authors |
1.33 | 3 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| J.D Horton | 1 | 11 | 1.33 |