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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
中文翻译:
最多具有 64n0.731 个 3 色的无三角形平面图
更新日期:2022-05-21
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 3-colorings. We improve his construction, giving examples of such graphs with at most 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3 着色。我们改进了他的结构,最多给出这样的图的例子3 着色。我们推测这个指数是最优的。