Geodesic
Decompositions of Cubic Traceable Graphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 35-49

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A traceable graph is a graph with a Hamilton path. The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular graph and a matching. We prove the conjecture for cubic traceable graphs.
Keywords: decomposition, cubic traceable graph, spanning tree, matching, 2-regular graph 
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Liu, Wenzhong; Li, Panpan. Decompositions of Cubic Traceable Graphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 35-49. http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a2/