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math.CO2026
The Erdős-Gallai bound for consecutive even cycle lengths
Yaobin Chen, Hong Liu, Xia Wang +2
Erdős and Gallai in 1959 proved the seminal result that every -vertex graph with no cycle of length at least has at most edges. We prove the extens…
math.CO2026
Small circumference in regular sublinear expanders
Yaobin Chen, Hong Liu, Xin Wei +1
Sublinear expansion is weak enough to be extracted from arbitrary graphs while retaining nearly all of their average degree, yet it has proved strong enough to force global structu…
math.CO2026
Strong invariants and Tverberg numbers in convexity spaces
Minho Cho, Andreas F. Holmsen, Attila Jung +1
Helly, Carathéodory, and Radon numbers encode three kinds of finite certificates in a convexity space: for the emptiness of an intersection, for membership in a convex hull, and fo…