During my ongoing studies I’ve done some research on various topics. Below are papers that I’ve coauthored.

## Upcoming

**Authors**: Bjarki Ágúst Guðmundsson, Tómas Ken Magnússon, Henning Ulfarsson

See source code at Github.

**Presented** at Permutation Patterns, Howard University, USA, June 2016 by Bjarki Ágúst Guðmundsson (Abstract, pg. 33)

**Authors**: M. Albert, C. Bean, A. Claesson, B. Gudmundsson, and H. Ulfarsson

See source code at Github.

**Presented** at ICE-TCS Seminar, Reykjavik University, Iceland, November 2014 by Christian Bean

**Presented** at Experimental Mathematics Seminar, Rutgers University, USA, March 2015 by Henning Ulfarsson (Video: Part 1, Part 2)

**Presented** at Permutation Patterns, Howard University, USA, June 2016 by Christian Bean (Abstract, pg. 10)

## 2015

**arXiv**: 1509.00099

**doi**: doi:10.1016/j.entcs.2016.03.013

**Authors**: Bjarki Ágúst Guðmundsson, Tómas Ken Magnússon, Björn Orri Sæmundsson

We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by pathwidth. We generalize bounds for defective coloring to weighted improper coloring and give a bound for weighted improper coloring in terms of the sum of edge weights. Finally we give fixed-parameter algorithms for weighted improper coloring both when parameterized by treewidth and maximum degree and when parameterized by treewidth and precision of edge weights. In particular, we obtain a linear-time algorithm for weighted improper coloring of interval graphs of bounded degree.

**Published** in Electronic Notes in Theoretical Computer Science, Volume 322, 18 April 2016, Pages 181-195

**Presented** at ICTCS 2015, the 16th Italian Conference on Theoretical Computer Science by Tómas Ken Magnússon

**Presented** at ICE-TCS Seminar, Reykjavik University, Iceland, 2015 by Tómas Ken Magnússon

## 2014

**arXiv**: 1404.3054

**Authors**: Michael Albert, Bjarki Gudmundsson, Henning Ulfarsson

The Collatz map is defined for a positive even integer as half that integer, and for a positive odd integer as that integer threefold, plus one. The Collatz conjecture states that when the map is iterated the number one is eventually reached. We study permutations that arise as sequences from this iteration. We show that permutations of this type of length up to 14 are enumerated by the Fibonacci numbers. Beyond that excess permutations appear. We will explain the appearance of these excess permutations and give an upper bound on the exact enumeration.

**Presented** at Stærðfræði á Íslandi, Iceland, 2013 by Bjarki Ágúst Guðmundsson

**Presented** at MIT Combinatorics Seminar, Boston, MA, October 2013 by Henning Ulfarsson

**Poster** at Permutation Patterns, East Tennessee State University, USA, July 2014 by Michael Albert (PDF)

**Presented** at the 2015 Joint Mathematics Meetings, San Antonio, TX by Michael Albert