论文标题
完整图的1型和2个规范子图的多色着色
Polychromatic colorings of 1-regular and 2-regular subgraphs of complete graphs
论文作者
论文摘要
如果$ g $是图形，而$ \ nathcal {h} $是$ g $的一组子图，我们说$ g $的边颜色为$ \ nathcal {h} $ - 如果每个图的$ \ nathcal {h} $中的每一个图形都会在其文章上均以$ g $ g $ g $ G $ G $ G $ G $ G $。 $ \ Mathcal {h} $ - $ g $的polyChromatic数字，表示为$ \ operatatorName {poly} _ \ Mathcal {h}（g）$，是$ \ Mathcal {h} $ - polyChromantic Coloring的$ \ Mathcal {h} $中最大的颜色。在本文中，我们确定$ g $ g $是$ g $是$ n $ dertices上的完整图，$ q $是固定的非负整数，$ \ m nartcal {h} $是三个家庭中的一家，至少是$ n-q n-q vertiess， $ n-q $顶点，以及所有长度为$ n-q $的周期的家族。在图中，Ramsey编号上的结果扩展了连接。
If $G$ is a graph and $\mathcal{H}$ is a set of subgraphs of $G$, we say that an edge-coloring of $G$ is $\mathcal{H}$-polychromatic if every graph from $\mathcal{H}$ gets all colors present in $G$ on its edges. The $\mathcal{H}$-polychromatic number of $G$, denoted $\operatorname{poly}_\mathcal{H} (G)$, is the largest number of colors in an $\mathcal{H}$-polychromatic coloring. In this paper we determine $\operatorname{poly}_\mathcal{H} (G)$ exactly when $G$ is a complete graph on $n$ vertices, $q$ is a fixed nonnegative integer, and $\mathcal{H}$ is one of three families: the family of all matchings spanning $n-q$ vertices, the family of all $2$-regular graphs spanning at least $n-q$ vertices, and the family of all cycles of length precisely $n-q$. There are connections with an extension of results on Ramsey numbers for cycles in a graph.
