Every planar graph is 5-choosable
Journal of Combinatorial Theory Series B
On the list dynamic coloring of graphs
Discrete Applied Mathematics
Note: Dynamic list coloring of bipartite graphs
Discrete Applied Mathematics
Note: On the dynamic coloring of graphs
Discrete Applied Mathematics
List dynamic coloring of sparse graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
On dynamic coloring for planar graphs and graphs of higher genus
Discrete Applied Mathematics
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A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. The dynamic chromatic number@g"d(G) of a graph G is the least number k such that G has a dynamic coloring with k colors. We show that @g"d(G)@?4 for every planar graph except C"5, which was conjectured in Chen et al. (2012) [5]. The list dynamic chromatic numberch"d(G) of G is the least number k such that for any assignment of k-element lists to the vertices of G, there is a dynamic coloring of G where the color on each vertex is chosen from its list. Based on Thomassen's (1994) result [14] that every planar graph is 5-choosable, an interesting question is whether the list dynamic chromatic number of every planar graph is at most 5 or not. We answer this question by showing that ch"d(G)@?5 for every planar graph.