Abstract
An acyclic \(k\)-coloring of a graph \(G\) is a \(k\)-coloring of its vertices such that no cycle of \(G\) is bichromatic. \(G\) is called acyclically \(k\)-colorable if it admits an acyclic \(k\)-coloring. In this paper, we prove that the generalized Petersen graph \(P(n,k)\) is acyclically 3-colorable except \(P(4,1)\) and the classical Petersen graph \(P(5,2)\).
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Acknowledgments
This work is supported by 973 Projects (2013CB32960, 2013CB329602,2010CB328103); National Natural Science Foundation of China Equipment (61127005); National Natural Science Foundation of China under Grant 60974112, 30970960.
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Zhu, E., Li, Z., Shao, Z. et al. Acyclic 3-coloring of generalized Petersen graphs. J Comb Optim 31, 902–911 (2016). https://doi.org/10.1007/s10878-014-9799-9
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DOI: https://doi.org/10.1007/s10878-014-9799-9