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math.CO2026
Exact Homomorphism Thresholds Beyond Cliques
Xinqi Huang, Mingyuan Rong, Chong Shangguan
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…
math.CO2026
Sharp asymptotic bounds for uniform union-free hypergraphs
Miao Liu, Chong Shangguan, Chenyang Zhang
An -uniform hypergraph is called -union-free if any two distinct subsets of at most edges have distinct union. The study of union-free hypergraphs has multiple origins an…