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arXiv · 1402.3741

On path-cycle decompositions of triangle-free graphs

Andrea Jiménez·Yoshiko Wakabayashi
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Abstract

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.

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Andrea Jiménez, Yoshiko Wakabayashi. 2017-10-23. On path-cycle decompositions of triangle-free graphs. https://doi.org/10.23638/dmtcs-19-3-7

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