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Triangle-free planar graphs with at most 64n0.731 3-colorings
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2022-05-20 , DOI: 10.1016/j.jctb.2022.05.003
Zdeněk Dvořák , Luke Postle

Thomassen conjectured that triangle-free planar graphs have exponentially many 3-colorings. Recently, he disproved his conjecture by providing examples of such graphs with n vertices and at most 215n/log2n 3-colorings. We improve his construction, giving examples of such graphs with at most 64nlog9/23<64n0.731 3-colorings. We conjecture this exponent is optimal.



中文翻译:

最多具有 64n0.731 个 3 色的无三角形平面图

Thomassen 猜想无三角形平面图的 3 着色指数呈指数增长。最近,他通过提供具有n个顶点且至多为215n/日志2n3 着色。我们改进了他的结构,最多给出这样的图的例子64n日志9/23<64n0.7313 着色。我们推测这个指数是最优的。

更新日期:2022-05-21
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