Martin Bachratý

collaborators

2 papers

math.CO2026

Vertex-transitive closures of graphs

Martin Bachratý, Grahame Erskine, Štefánia Glevitzká +2

A vertex-transitive closure of $Γ$ is a vertex-transitive supergraph of $Γ$ on the same vertex set. The vertex-transitive number of a graph $Γ$ , denoted by $d_{v t} (Γ)$ , is the smal…

math.CO2017

Asymptotically approaching the Moore bound for diameter three by Cayley graphs

Martin Bachratý, Jana Šiagiová, Jozef Širáň

The largest order $n (d, k)$ of a graph of maximum degree $d$ and diameter $k$ cannot exceed the Moore bound, which has the form $M (d, k) = d^{k} - O (d^{k - 1})$ for $d \to \infty$ and any fi…