The aim of this paper is to construct new small regular graphs with girth $7$ using integer programming techniques. Over the last two decades solvers for integer programs have become more and more powerful and have proven to be a useful aid for many hard combinatorial problems. Despite successes in many related fields, these optimisation tools have so far been absent in the quest for small regular graphs with a given girth. Here we illustrate the power of these solvers as an aid to construct small regular girth $7$ graphs from girth $8$ cages.
@article{10_37236_4854,
author = {Frans J.C.T. de Ruiter and Norman L. Biggs},
title = {Applications of integer programming methods to cages},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/4854},
zbl = {1329.05152},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4854/}
}
TY - JOUR
AU - Frans J.C.T. de Ruiter
AU - Norman L. Biggs
TI - Applications of integer programming methods to cages
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/4854/
DO - 10.37236/4854
ID - 10_37236_4854
ER -
%0 Journal Article
%A Frans J.C.T. de Ruiter
%A Norman L. Biggs
%T Applications of integer programming methods to cages
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/4854/
%R 10.37236/4854
%F 10_37236_4854
Frans J.C.T. de Ruiter; Norman L. Biggs. Applications of integer programming methods to cages. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/4854
