论文标题
通过三角计数的三种着色
Three coloring via triangle counting
论文作者
论文摘要
在第一个部分的结果中，艾伯特（Abbott）和周（Abbott and Zhou）使用计数参数表明，每个平面图4至11的循环都可以3色。在其证明中隐含的是关于平面图的事实：在任何最低度3的平面图中，如果没有两个三角形共享边缘，则三角形严格占面部的2/3。我们展示了该结果如何与Kostochka和Yancey对矿石对K = 4的猜想的分辨率相结合，这意味着每个平面图没有长度4到8的循环，都是3个色彩的。
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Zhou used a counting argument to show that every planar graph without cycles of lengths 4 through 11 is 3-colorable. Implicit in their proof is a fact about plane graphs: in any plane graph of minimum degree 3, if no two triangles share an edge, then triangles make up strictly less than 2/3 of the faces. We show how this result, combined with Kostochka and Yancey's resolution of Ore's conjecture for k = 4, implies that every planar graph without cycles of lengths 4 through 8 is 3-colorable.
