# Seminars & Colloquia Calendar

## On the hardness of coloring rainbow-colorable hypergraphs

#### Aditya Potukuchi, Rutgers

Location: ** Hill 705**

Date & time: Monday, 02 April 2018 at 2:00PM - 3:00PM

Abstract: A (uniform) hypergraph is c-colorable if its vertices can be assigned colors from 1,...,c so that no hyperedge is monochromatic. A hypergraph is r-rainbow colorable (or r-polychromatic) if its vertices can be assigned colors from 1,...,r so that every edge has all r colors. It is very easy to see that if a hypergraph is r-rainbow colorable for r geq 2, then it is 2-colorable. However, given a hypergraph with the promise that is r-rainbow colorable for r geq 2, finding an efficient algorithm that outputs a proper 2-coloring of it does not always seem to be an easy problem. This result shows that finding a c-coloring of a k-uniform, k(1 - o_c(1))-rainbow colorable hypergraph is NP-hard. The gadgets involved in the reduction are some kinds of variations/generalizations of the Kneser hypergraph, some of which seem to be well studied, and some which are not (as far as we know).

This is based on joint work with Per Austrin and Amey Bhangale.

R. Shapiro Organizer's Page

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

Organizer's webpage: Organizer's webpage

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