Decomposition of a graph into paths: structural and algorithmic aspects
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| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed Rio de Janeiro, Programa Engn Sistemas & Comp, Rio De Janeiro - Brazil
[2] Univ Valparaiso, CIMFAV, Fac Ingn, Valparaiso - Chile
[3] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | DISCRETE MATHEMATICS; v. 342, n. 5, p. 1403-1414, MAY 2019. |
| Web of Science Citations: | 3 |
| Abstract | |
A path decomposition of a graph G is a collection of edge-disjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admits a path decomposition of cardinality at most left perpendicular(n + 1)/2right perpendicular. Gallai's Conjecture has been verified for many classes of graphs. In particular, Lovasz (1968) verified this conjecture for graphs with at most one vertex with even degree, and Pyber (1996) verified it for graphs in which every cycle contains a vertex with odd degree. Recently, Bonamy and Perrett (2016) verified Gallai's Conjecture for graphs with maximum degree at most 5, and Botler et al. (2017) verified it for graphs with treewidth at most 3. In this paper, we verify Gallai's Conjecture for triangle-free planar graphs. (C) 2019 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 17/23623-4 - Partition problems in graphs and digraphs |
| Grantee: | Maycon Sambinelli |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |