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math.CO2024
The Lonely Runner Conjecture turns 60
Guillem Perarnau, Oriol Serra
The Lonely Runner Conjecture originated in Diophantine approximation is turning 60. Even if the conjecture is still widely open, the flow of partial results, innovative tools and c…
math.CO2024
First Order Logic of Sparse Graphs with Given Degree Sequences
Alberto Larrauri, Guillem Perarnau
We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set…