Botler, FabioJimenez, AndreaSambinelli, MayconWakabayashi, Yoshiko2022-11-302022-11-302021http://repositoriobibliotecas.uv.cl/handle/uvscl/7248The 2-Decomposition Conjecture, equivalent to the 3-Decomposition Conjecture stated in 2011 by Hoffmann-Ostenhof, claims that every connected graph G with vertices of degree 2 and 3, and satisfying that G - E(C) is disconnected for every cycle C, admits a decomposition into a spanning tree and a matching. In this work we show that the 2-Decomposition Conjecture holds for graphs whose vertices of degree 3 induce a collection of cacti in which each vertex belongs to a cycle.Under a Creative Commons licenseGRAPH DECOMPOSITIONCUBIC GRAPHS3-DECOMPOSITION CONJECTUREHISTSPANNING TREESArticulohttps://doi.org/10.1016/j.procs.2021.11.044