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math.CO2026
Random 0/1-polytopes expand rapidly
He Guo, István Tomon
A 0/1-polytope is the convex hull of a subset . A celebrated conjecture of Mihail and Vazirani asserts that the graph of every 0/1-polytope has edge-expansion…
math.CO2025
Short rainbow cycles for families of small edge sets
He Guo
In 2019, Aharoni proposed a conjecture generalizing the Caceetta-Häggkvist conjecture: if an -vertex graph admits an edge coloring (not necessarily proper) with colors s…
math.CO2024
The list chromatic number of the intersection of two generalized partition matroids
He Guo
A famous theorem of Galvin states that the list chromatic number of the intersection of two partition matroids equals its chromatic number. Kiraly and Berczi et. al. conjectured th…