Stefan Glock

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math.CO2025

On Kotzig's conjecture in random graphs

Stefan Glock, Amedeo Sgueglia

In 1963, Anton Kotzig famously conjectured that $K_{n}$ , the complete graph of order $n$ , where $n$ is even, can be decomposed into $n - 1$ perfect matchings such that every pair of…

math.CO2023

Optimal Hamilton covers and linear arboricity for random graphs

Nemanja Draganić, Stefan Glock, David Munhá Correia +1

In his seminal 1976 paper, Pósa showed that for all $p \geq C lo g n / n$ , the binomial random graph $G (n, p)$ is with high probability Hamiltonian. This leads to the following natural…

math.CO2023

Hamilton cycles in pseudorandom graphs

Stefan Glock, David Munhá Correia, Benny Sudakov

Finding general conditions which ensure that a graph is Hamiltonian is a central topic in graph theory. An old and well known conjecture in the area states that any $d$ -regular $n$ …