In this paper we give new bounds on the bisection width of random 3-regular graphs on $n$ vertices. The main contribution is a new lower bound of $0.103295n$ based on a first moment method together with a structural analysis of the graph, thereby improving a 27-year-old result of Kostochka and Melnikov. We also give a complementary upper bound of $0.139822n$ by combining a result of Lyons with original combinatorial insights. Developping this approach further, we obtain a non-rigorous improved upper bound with the help of Monte Carlo simulations.
@article{10_37236_11085,
author = {Lyuben Lichev and Dieter Mitsche},
title = {On the minimum bisection of random 3-regular graphs},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11085},
zbl = {1517.05160},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11085/}
}
TY - JOUR
AU - Lyuben Lichev
AU - Dieter Mitsche
TI - On the minimum bisection of random 3-regular graphs
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11085/
DO - 10.37236/11085
ID - 10_37236_11085
ER -
%0 Journal Article
%A Lyuben Lichev
%A Dieter Mitsche
%T On the minimum bisection of random 3-regular graphs
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11085/
%R 10.37236/11085
%F 10_37236_11085
Lyuben Lichev; Dieter Mitsche. On the minimum bisection of random 3-regular graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11085
