Planar graphs are 9/2-colorable

Daniel W. Cranston; Landon Rabern

Planar graphs are 9/2-colorable

Combinatorics 2019-11-18 v3

Authors: Daniel W. Cranston , Landon Rabern

Abstract

We show that every planar graph $G$ has a 2-fold 9-coloring. In particular, this implies that $G$ has fractional chromatic number at most $\frac92$ . This is the first proof (independent of the 4 Color Theorem) that there exists a constant $k<5$ such that every planar $G$ has fractional chromatic number at most $k$ .

Keywords

graph coloring rainbow coloring ramsey theory and colorings

Cite

@article{arxiv.1410.7233,
  title  = {Planar graphs are 9/2-colorable},
  author = {Daniel W. Cranston and Landon Rabern},
  journal= {arXiv preprint arXiv:1410.7233},
  year   = {2019}
}

Comments

12 pages, 6 figures; following the suggestion of an editor, we split the original version of this paper into two papers: one is the current version of this paper, and the other is "Planar graphs have Independence Ratio at least 3/13" (also available on the arXiv)

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