AI 中文总结
研究在\(n\)顶点的\(\bigcup_{i = 1}^t F_i -\)自由图中，对于\(2\leq s\leq r\)和足够大的\(n\)，确定具有最大\(s -\)团谱半径的唯一极值图这一问题，核心方法未提及，主要贡献是得出上述结论。
AI 中文摘要
对于给定图\(F\)，不含\(F\)作为子图的图\(G\)称为\(F -\)自由图。若删除一条边会降低色数，则该图是颜色临界的。设\(F_1,F_2,\cdots,F_t\)是\(t\)个不相交的色数为\(r + 1\)的颜色临界图。对于\(2\leq s\leq r\)和足够大的\(n\)，确定了在所有\(n\)顶点的\(\bigcup_{i = 1}^t F_i -\)自由图中具有最大\(s -\)团谱半径的唯一极值图。
英文摘要
For a given graph $F$, a graph $G$ is called $F$-free if it does not contain $F$ as a subgraph. A graph is color-critical if deleting one of its edges decreases its chromatic number. Let $F_1, F_2, \cdots, F_t$ be $t$ disjoint color-critical graphs with chromatic number $r+1$. For $2 \leq s \leq r$ and sufficiently large $n$, we determine the unique extremal graph with the maximum $s$-clique spectral radius among all $n$-vertex $\bigcup_{i=1}^t F_i$-free graphs.
