University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Extremal Cuts and Isoperimetry in Random Cubic Graphs

Extremal Cuts and Isoperimetry in Random Cubic Graphs

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If you have a question about this talk, please contact Guillem Perarnau.

Random 3-regular graphs are a particularly simple random structure, the bisection of (general) cubic graphs plays a role in the construction of efficient exponential-time algorithms, and it seems likely that random cubic graphs are extremal. It is known that a random cubic graph has a (minimum) bisection of size at most 1/6 times its order (indeed this is known for all cubic graphs), and we reduce this to below 1/7 (to 0.13993) by analyzing an algorithm with a couple of surprising features. We increase the corresponding lower bound on minimum bisection (from 1/9.9 to 0.10133) using the Hamilton cycle model of a random cubic graph. We use the same Hamilton cycle approach to decrease the upper bound on maximum cut (from 1.4026 to 1.40031). We will discuss some related conjectures.

This talk is part of the Combinatorics and Probability seminar series.

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