Jiménez, Andrea and Wakabayashi, Yoshiko - On path-cycle decompositions of triangle-free graphs

dmtcs:659 - Discrete Mathematics & Theoretical Computer Science, October 26, 2017, Vol. 19 no. 3 - https://doi.org/10.23638/DMTCS-19-3-7
On path-cycle decompositions of triangle-free graphs

Authors: Jiménez, Andrea and Wakabayashi, Yoshiko

In this work, we study conditions for the existence of length-constrained path-cycle decompositions, that is, partitions of the edge set of a graph into paths and cycles of a given minimum length. Our main contribution is the characterization of the class of all triangle-free graphs with odd distance at least $3$ that admit a path-cycle decomposition with elements of length at least $4$. As a consequence, it follows that Gallai's conjecture on path decomposition holds in a broad class of sparse graphs.

Volume: Vol. 19 no. 3
Section: Graph Theory
Published on: October 26, 2017
Submitted on: September 30, 2016
Keywords: Mathematics - Combinatorics,05C38, 05C05, 05C10, 05C75,G.2.2

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