Spring 2019

A Ramsey-type Theorem on the Max-Cut Value of d-Regular Graphs *starts at 10:30 a.m. sharp*

Wednesday, Mar. 27, 2019 10:30 am12:00 pm PDT

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Parent Program: 

Charles Anthony Carlson (University of Colorado, Boulder)


Room 116

We consider the problem of finding large cuts in graphs that contain no small cliques. We show that for any r >= 3, every k_r-free graphs with maximum degree d has a cut that cuts at least a 1/2 + Ω(1/d^{1-1/2^{r-2}}) fraction of its edges. This generalizes a result of Shearer that shows every triangle-free d-regular graph has a cut that cuts at least a 1/2 + Ω(1/\sqrt{d}) fraction of its edges. Our proof yields a randomized polynomial-time algorithm.