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

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

Talks@bham, University of Birmingham. Contact Us | Help and Documentation | Privacy and Publicity.
talks@bham is based on talks.cam from the University of Cambridge.