Planar graphs have two-coloring number at most 8
Zden\v{e}k Dvo\v{r}\'ak, Adam Kabela, Tom\'a\v{s} Kaiser
TL;DR
This paper proves that the two-coloring number of any planar graph is at most 8, resolving a longstanding open question and establishing an optimal bound for this graph property.
Contribution
It establishes the first proven upper bound of 8 for the two-coloring number of planar graphs, confirming the bound's optimality.
Findings
Two-coloring number of planar graphs is at most 8
The bound of 8 is proven to be tight
Resolved a question posed by Kierstead et al.
Abstract
We prove that the two-colouring number of any planar graph is at most 8. This resolves a question of Kierstead et al. [SIAM J. Discrete Math.~23 (2009), 1548--1560]. The result is optimal.
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