# Selected Publications

### Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs

Since 1997 a considerable effort has been spent on the study of the swap (switch) Markov chains on graphic degree sequences. All of these results assume some kind of regularity in the corresponding degree sequences. Recently, Greenhill and Sfragara published a breakthrough paper about irregular simple and directed degree sequences for which rapid mixing of the MCMC is known (for e.g., scale-free graphs with $\gamma>2.5$). In this paper we present two group of theorems. The first one contains a result similar to the theorem of GS for bipartite degree sequences, which slightly improve their result on directed degree sequences. The second group presents another vast region of bipartite degree sequences with rapidly mixing MCMC sampling process.
PLOS ONE, 2018

### Mobile vs. point guards

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using “rectangular vision”. We prove a sharp bound on the minimum number of point guards required to cover the gallery in terms of the minimum number of vertical mobile guards and the minimum number of horizontal mobile guards required to cover the gallery. Furthermore, we show that the latter two numbers can be computed in linear time.
Accepted in Discrete Comput. Geom., 2018

# Recent & Upcoming Talks

Doctoral Dissertation Defense
Friday, November 17, 2017 10:00
Mobile vs. point guards in orthogonal art gallery theorems
Friday, May 19, 2017 14:25
Art gallery theorems
Wednesday, November 4, 2015 14:00

# Recent Posts

### A note on the Erdős-Selfridge potential

The following small result has been sitting untouched in my research folder since December, 2014. As I have not been able to produce other interesting results in the field it has remained unpublished until now. A hypergraph is properly 2-colorable if its vertex set can be colored blue and red such that there is no monochromatic edge. Lemma 1 (TRM, 2014). Let $\mathcal{H}$ be an $r$-uniform hypergraph on $n$ vertices.

## Welcome to my homepage!

I have created this website using Hugo and the Academic theme. Content is served by Apache over HTTPS using a certificate from Let’s Encrypt. These free software have allowed me to deploy the site quickly, but I have yet to come up with a plan to avoid the Javascript trap.

# Contact

## Instant messaging

Wire: @tamasrobertmezei

[matrix]: @tomi:kormi.hu

## E-mail

mezei.tamas.robert@renyi.mta.hu

tamasrobert.mezei@gmail.com