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math.CO2026
The replica symmetric solution for hypergraph independent sets in the critical regime
Matthew Jenssen, Will Perkins, Aditya Potukuchi +1
We prove a variational formula for the logarithmic asymptotics of a non-existence probability in a broad class of combinatorial problems such as avoiding cliques in random graphs a…
math.CO2025
On fractional triangle decompositions of random graphs
Ghaura Mahabaduge, Michael Simkin
We prove that with high probability with admits a fractional triangle decomposition (FTD), i.e., a nonnegative weighting of its triangles such th…
math.CO2023
Ramsey and Turán numbers of sparse hypergraphs
Jacob Fox, Maya Sankar, Michael Simkin +2
Degeneracy plays an important role in understanding Turán- and Ramsey-type properties of graphs. Unfortunately, the usual hypergraphical generalization of degeneracy fails to captu…