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math.CO2026
Optimal girth-dependent bounds for the Bethe approximation of the permanent
Dingding Dong, Vishesh Jain
For an nonnegative matrix , the Bethe permanent, which is computable in deterministic polynomial time, satisfies the tight universal comparison \[\operatorname{Bethe…
math.CO2026
Range of random -homomorphisms on weak expanders
Dingding Dong, Jinyoung Park
We prove that random -homomorphisms on weakly expanding bipartite graphs exhibit a strong "flatness" phenomenon. Extending prior work of Peled, Samotij, and Yehudayoff…
math.CO2025
Even-degeneracy of a random graph
Ting-Wei Chao, Dingding Dong, Zixuan Xu
A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the Erdős--Renyi…