A subdivision of complete graph K_n is any graph that can be obtained from K_n by replacing edges of K_n by chains of two edges (every such chain adds to the graph a new vertex of degree 2). Let G be a connected graph with maximal vertex degree d, d ≥ 8. We prove that there is a proper dynamic vertex coloring of G with d colors iff G is distinct from K_d+1 and its subdivisions. Bibliography: 7 titles.