Dynamic coloring of graphs having no K5K5 minor

We prove that every simple connected graph with no K5K5 minor admits a proper 4-coloring such that the neighborhood of each vertex vv 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].