6 papers
On the order-diameter ratio of girth-diameter cages
Stijn Cambie, Jan Goedgebeur, Jorik Jooken +1
For integers , a -cage (or simply girth-diameter cage) is a smallest -regular graph of girth and diameter (if it exists). The order of a -cage i…
On the number of perfect matchings in planar graphs
Jan Goedgebeur, Jorik Jooken, Tibo Van den Eede +1
We investigate the minimum non-zero number of perfect matchings in planar graphs. We prove that this is a constant for 2-connected planar graphs of minimum degree 3 and 3-connected…
The Gray graph is pseudo 2-factor isomorphic
Marien Abreu, Jan Goedgebeur, Jorik Jooken +2
A graph is pseudo 2-factor isomorphic if all of its 2-factors have the same parity of number of cycles. Abreu et al. [J. Comb. Theory, Ser. B. 98 (2008) 432--442] conjectured that…
New small regular graphs of given girth: the cage problem and beyond
Geoffrey Exoo, Jan Goedgebeur, Jorik Jooken +2
The cage problem concerns finding -graphs, which are -regular graphs with girth , of the smallest possible number of vertices. The central goal is to determine $n(k,g)…
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 , the maximum size (number of edges) of an -vertex graph of girth at least 5. The core of our algorit…
Computational methods for finding bi-regular cages
Jan Goedgebeur, Jorik Jooken, Tibo Van den Eede
An -graph is a (simple, undirected) graph of girth with vertices of degrees and where . Given , we seek the -graphs…