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Splitting Planar Graphs of Girth 6 into Two Linear Forests with Short Paths
[article]
2015
arXiv
pre-print
Recently, Borodin, Kostochka, and Yancey (On 1-improper 2-coloring of sparse graphs. Discrete Mathematics, 313(22), 2013) showed that the vertices of each planar graph of girth at least 7 can be 2-colored so that each color class induces a subgraph of a matching. We prove that any planar graph of girth at least 6 admits a vertex coloring in 2 colors such that each monochromatic component is a path of length at most 14. Moreover, we show a list version of this result. On the other hand, for each
arXiv:1507.02815v1
fatcat:7a75jrmcn5g3bkijf7lizqd5wq