On the minimum bisection of random $3$-regular graphs

Lyuben Lichev; Dieter Mitsche

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arXiv · 2009.00598

On the minimum bisection of random $3$-regular graphs

Lyuben Lichev·Dieter Mitsche

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Abstract

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.

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BibTeX RIS

Lyuben Lichev, Dieter Mitsche. 2020-09-01. On the minimum bisection of random $3$-regular graphs. https://arxiv.org/abs/2009.00598

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