T. V. D. Eede

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math.CO2025

On the order-diameter ratio of girth-diameter cages

Stijn Cambie, Jan Goedgebeur, Jorik Jooken +1

For integers $k, g, d$ , a $(k; g, d)$ -cage (or simply girth-diameter cage) is a smallest $k$ -regular graph of girth $g$ and diameter $d$ (if it exists). The order of a $(k; g, d)$ -cage i…

math.CO2025

Improved lower bounds on the maximum size of graphs with girth 5

Jan Goedgebeur, Jorik Jooken, Gwenaël Joret +1

We present a new algorithm for improving lower bounds on $e x (n; {C_{3}, C_{4}})$ , the maximum size (number of edges) of an $n$ -vertex graph of girth at least 5. The core of our algorit…

math.CO2024

Computational methods for finding bi-regular cages

Jan Goedgebeur, Jorik Jooken, Tibo Van den Eede

An $({r, m}; g)$ -graph is a (simple, undirected) graph of girth $g \geq 3$ with vertices of degrees $r$ and $m$ where $2 \leq r < m$ . Given $r, m, g$ , we seek the $({r, m}; g)$ -graphs…