Adrian Beker

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20202026

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3 papers · 1 filter

math.CO2026

The inverse problem for the Steiner-Wiener index of trees

Adrian Beker, Rudi Mrazović

For a connected graph $G$ and a set $S \subset V (G)$ , the Steiner distance $d_{G} (S)$ is the minimum number of edges in a connected subgraph of $G$ containing $S$ . The Steiner-Wiener…

math.CO2026

A note on the shortest law for the symmetric group

Adrian Beker, Luka Milićević, Rudi Mrazović

Let $α (n)$ denote the length of the shortest non-trivial two-variable law for the symmetric group $S_{n}$ . Buskin's quantitative subgroup-separability argument gives the classical lo…

math.CO2020

The star avoidance game

Adrian Beker

Let $n, k$ be positive integers. The $(k + 1)$ -star avoidance game on $K_{n}$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete g…