
Every toroidal graph without triangles adjacent to 5cycles is DP4colorable
DPcoloring, also known as correspondence coloring, is introduced by Dvo...
03/03/2018 ∙ by Tao Wang, et al. ∙ 0 ∙ shareread it

DP4coloring of planar graphs with some restrictions on cycles
DPcoloring was introduced by Dvořák and Postle as a generalization of l...
09/17/2019 ∙ by Rui Li, et al. ∙ 0 ∙ shareread it

On the Chromatic Polynomial and Counting DPColorings
The chromatic polynomial of a graph G, denoted P(G,m), is equal to the n...
04/16/2019 ∙ by Hemanshu Kaul, et al. ∙ 0 ∙ shareread it

Flexibility of planar graphs without 4cycles
Proper graph coloring assigns different colors to adjacent vertices of t...
03/04/2019 ∙ by Tomáš Masařík, et al. ∙ 0 ∙ shareread it

Addressing Johnson graphs, complete multipartite graphs, odd cycles and other graphs
Graham and Pollak showed that the vertices of any graph G can be address...
08/14/2018 ∙ by Sebastian M. Cioabă, et al. ∙ 0 ∙ shareread it

Flexibility of planar graphs of girth at least six
Let G be a planar graph with a list assignment L. Suppose a preferred co...
02/11/2019 ∙ by Zdeněk Dvořák, et al. ∙ 0 ∙ shareread it

Propagation time for probabilistic zero forcing
Zero forcing is a coloring game played on a graph that was introduced mo...
12/24/2018 ∙ by Jesse Geneson, et al. ∙ 0 ∙ shareread it
3choosable planar graphs with some precolored vertices and no 5^cycles normally adjacent to 8^cycles
DPcoloring was introduced by Dvořák and Postle [J. Combin. Theory Ser. B 129 (2018) 38–54] as a generalization of list coloring. They used a "weak" version of DPcoloring to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of length 4 to 8 is 3choosable. Liu and Li improved the result by showing that every planar graph without adjacent cycles of length at most 8 is 3choosable. In this paper, it is showed that every planar graph without 5^cycles normally adjacent to 8^cycles is 3choosable. Actually, all these three papers give more stronger results by stating them in the form of "weakly" DP3coloring and color extension.
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