AI 中文总结
该研究针对单个非完全禁图精确同态阈值未知的问题，将团情形扩展至更大禁图族，确定了该族中每一个图的精确同态阈值。
AI 中文摘要
色阈值源于Erdős和Simonovits的问题，探究线性最小度条件何时迫使H-自由图具有有界色数。受Thomassen问题启发，同态阈值要求更强结论：每一个此类图都存在到有界阶H-自由图的同态。自Goddard和Lyle确定团情形后，单个非完全禁图的精确同态阈值仍未知。本文将团情形扩展至更大的禁图族，确定该族中每一个图的同态阈值精确值。
英文摘要
The chromatic threshold, originating in a question of Erdős and Simonovits, asks when a linear minimum-degree condition forces bounded chromatic number in H-free graphs. Motivated by a question of Thomassen, the homomorphism threshold asks for the stronger conclusion that every such graph admits a homomorphism to an H-free graph of bounded order. Since the work of Goddard and Lyle determined the clique case, exact homomorphism thresholds for individual non-complete forbidden graphs have remained unknown. In this paper, we extend the clique case to a larger family of forbidden graphs, determining the homomorphism threshold exactly for every graph in this family.
Comments19 pages, no figures
