The 2-Decomposition Conjecture for a new class of graphs

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2021

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Elsevier

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Resumen

The 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.

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GRAPH DECOMPOSITION, CUBIC GRAPHS, 3-DECOMPOSITION CONJECTURE, HIST, SPANNING TREES

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Under a Creative Commons license

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