Resolvable path designs
| dc.contributor.author | Horton, J., D. | |
| dc.date.accessioned | 2023-03-01T18:28:16Z | |
| dc.date.available | 2023-03-01T18:28:16Z | |
| dc.date.issued | 1983 | |
| dc.description.abstract | A resolvable (balanced) path design, RBPD (v,k,) is the decomposition of λ copies of the complete graph on v vertices into edge-disjoint subgraphs such that each subgraph consists of v /k 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 v/3. 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 1cm(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 Hell and Rosa. | |
| dc.description.copyright | Copyright @ J. D. Horton, 1983. | |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/14830 | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Computer Science | |
| dc.title | Resolvable path designs | |
| dc.type | technical report |
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