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math.CO2026
Minimising the harmonic sum of cycle lengths
Richard Montgomery, Aleksa Milojević, Alexey Pokrovskiy +1
A central theme in extremal graph theory is to understand the relationship between the density of a graph and the richness of its cycle length spectrum, which is the set of distinc…
math.CO2026
Breaking the Bollobás-Eldridge-Catlin Barrier for Bipartite Graphs
Peter Allen, Julia Böttcher, Jozef Skokan +1
The celebrated Bollobás-Eldridge-Catlin packing conjecture states that every -vertex graph with minimum degree at least contains every -vert…
math.CO2026
Nearly-uniform degree distributions in spanning subgraphs
Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov
We show that, when , every -regular -vertex graph contains a spanning subgraph whose degree distribution is nearly uniform, i.e., for each , there are…