AI 中文总结
研究广义四边形超图的上色数，通过将点和线对应顶点和超边，定义彩虹着色与无彩虹着色，进而确定给定超图\(H\)的上色数\(\overline{\chi}(H)\)。
AI 中文摘要
我们可将广义四边形视为一种超图，其中点和线分别对应超图的顶点和超边。若超边上所有顶点被赋予两两不同颜色，则称该顶点着色在该超边上为彩虹着色；若不存在彩虹边，则称该着色为无彩虹着色。对于给定超图\(H\)，存在无彩虹\(k -\)着色的最大整数\(k\)称为\(H\)的上色数，记为\(\overline{\chi}(H)\)。
英文摘要
We can regard a generalized quadrangle as a hypergraph in which points and lines are identified with vertices and hyperedges, respectively. A vertex coloring is said to be rainbow on a hyperedge if all vertices contained in that hyperedge are assigned pairwise distinct colors; if no hyperedge is rainbow, the coloring is termed rainbow-free. For a given hypergraph $H$, the maximum integer $k$ for which there exists a rainbow-free $k$-coloring is called the upper chromatic number of $H$, and is denoted by $\overlineχ(H)$.
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