We prove that every simple connected graph with no K 5 minor admits a proper 4-coloring such that the neighborhood of each vertex v having more than one neighbor is not monochromatic, unless the graph is isomorphic to the cycle of length 5. This generalizes the result on planar graphs by S.-J. Kim, W.-J. Park and the second author Discrete Appl. Math. 161 (2013) 2207-2212.
['Youn-Jin Kim', 'Sang June Lee', 'Sang-il Oum']
Dynamic coloring of graphs having no K 5 minor