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math.CO2025
On Kotzig's conjecture in random graphs
Stefan Glock, Amedeo Sgueglia
In 1963, Anton Kotzig famously conjectured that , the complete graph of order , where is even, can be decomposed into perfect matchings such that every pair of…
math.CO2025
Steiner triple systems with high discrepancy
Lior Gishboliner, Stefan Glock, Amedeo Sgueglia
In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed and , any -co…
math.CO2025
Defect and transference versions of the Alon-Frankl-Lovasz theorem
Lior Gishboliner, Stefan Glock, Peleg Michaeli +1
Confirming a conjecture of Erdős on the chromatic number of Kneser hypergraphs, Alon, Frankl and Lovász proved that in any -colouring of the edges of the complete -uniform hy…