On Gallai's and Hajós' Conjectures for graphs with treewidth at most 3

Fábio Botler, Maycon Sambinelli, Rafael S. Coelho +1

A path (resp. cycle) decomposition of a graph $G$ is a set of edge-disjoint paths (resp. cycles) of $G$ that covers the edge set of $G$. Gallai (1966) conjectured that every graph…