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arXiv · 1901.11339

Decomposition of cubic graphs related to Wegner's conjecture

János Barát
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Abstract

Thomassen formulated the following conjecture: Every $3$-connected cubic graph has a red-blue vertex coloring such that the blue subgraph has maximum degree $1$ (that is, it consists of a matching and some isolated vertices) and the red subgraph has minimum degree at least $1$ and contains no $3$-edge path. We prove the conjecture for Generalized Petersen graphs. We indicate that a coloring with the same properties might exist for any subcubic graph. We confirm this statement for all subcubic trees.

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János Barát. 2019-01-31. Decomposition of cubic graphs related to Wegner's conjecture. https://arxiv.org/abs/1901.11339

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