Painting Squares in $\Delta^2-1$ Shades

Daniel W. Cranston; Landon Rabern

Painting Squares in $\Delta^2-1$ Shades

Combinatorics 2017-05-15 v2

Authors: Daniel W. Cranston , Landon Rabern

Abstract

Cranston and Kim conjecture that if $G$ is a connected graph with maximum degree $\Delta$ and $G$ is not a Moore Graph, then $\chi_l(G^2) \le \Delta^2-1$ ; here $\chi_l$ is the list chromatic number. We prove their conjecture; in fact, this upper bound holds even for online list chromatic number.

Keywords

list chromatic number square of a graph maximum degree Moore graph online list coloring graph coloring conjecture

Cite

@article{arxiv.1311.1251,
  title  = {Painting Squares in $\Delta^2-1$ Shades},
  author = {Daniel W. Cranston and Landon Rabern},
  journal= {arXiv preprint arXiv:1311.1251},
  year   = {2017}
}

Comments

23 pages, 10 figures. In version 2, we add a conjecture and 2 figures to the introduction. Results are unchanged

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