Document Type

Article

Publication Date

February 2018

Keywords

coloring of graphs and hypergraphs, planar graphs

Disciplines

Discrete Mathematics and Combinatorics

Abstract

The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min{k, d(v)} colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.

Comments

This work can also be found on arxiv.org at this link.

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