论文标题
在边缘彩色完整的完整图中，没有单色三角形：顶点 - 庞克类似结果
Properly colored cycles in edge-colored complete graphs containing no monochromatic triangles: a vertex-pancyclic analogous result
论文作者
论文摘要
边缘颜色图中正确的彩色循环（路径）是一个循环（路径），其连续边缘分配了不同的颜色。单色三角形是一个长度为3 $的周期，边缘分配了相同的颜色。众所周知，每个边缘颜色的完整图都不包含单色三角形，总是包含正确的汉密尔顿路径。在本文中，我们研究了当禁止单色三角形时，在边彩色完整图中存在正确的彩色循环。我们获得了一个顶点 - 庞术类似结果，并结合了所有异常的表征。
A properly colored cycle (path) in an edge-colored graph is a cycle (path) with consecutive edges assigned distinct colors. A monochromatic triangle is a cycle of length $3$ with the edges assigned a same color. It is known that every edge-colored complete graph without containing monochromatic triangles always contains a properly colored Hamilton path. In this paper, we investigate the existence of properly colored cycles in edge-colored complete graphs when monochromatic triangles are forbidden. We obtain a vertex-pancyclic analogous result combined with a characterization of all the exceptions.
