| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | DISCRETE MATHEMATICS; v. 338, n. 11, p. 1845-1855, NOV 6 2015. |
| Web of Science Citations: | 4 |
| Abstract | |
A P-k-decomposition of a graph G is a set of edge-disjoint paths with k edges that cover the edge set of G. Kotzig (1957) proved that a 3-regular graph admits a P-3-decomposition if and only if it contains a perfect matching. Kotzig also asked what are the necessary and sufficient conditions for a (2k+1)-regular graph to admit a decomposition into paths with 2k + 1 edges. We partially answer this question for the case k = 2 by proving that the existence of a perfect matching is sufficient for a triangle-free 5-regular graph to admit a P-5-decomposition. This result contributes positively to the conjecture of Favaron et al. (2010) that states that every (2k+1)-regular graph with a perfect matching admits a P2k+1-decomposition. (C) 2015 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 11/08033-0 - Decomposition of a graph into paths: structural and algorithmic aspects |
| Grantee: | Fábio Happ Botler |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 13/11431-2 - Extremal and probabilistic combinatorics |
| Grantee: | Guilherme Oliveira Mota |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 14/01460-8 - Graph decompositions |
| Grantee: | Fábio Happ Botler |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 13/20733-2 - Extremal and probabilistic combinatorics |
| Grantee: | Guilherme Oliveira Mota |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |