Klas Markström

I am Associate Professor in Mathematics at Umeå University. My main area of research is graph theory and combinatorics. Here I study both deterministic structural problems and problems regarding the pr

Journal of Graph theory 88, no 3, p.411-427. Abstract Let be a graph of density p on n vertices. Following Erdős, Łuczak, and Spencer, an m‐vertex subgraph H of G is called fullif H has minimum degree at lea. Let denote the order of a largest of G. If is a nonnegative integer, define

Combinatorics, Probability and Computing, 1-21. doi:10.1017/S096354831800055X, Cambridge University Press. Abstract An n × n partial Latin square P is called α-dense if each row and column has at most αnnon-emp times in . An × array where each cell contains a subset of {1,…, } is a (, ) -array if each symbol occurs at most times in each row and column and each cell contains a set of size at most . Combining the notions of completing partial Latin squares and avoiding arrays, we prove that there are constants , > 0 such that, for every positive integer , if is an -dense × partial Latin square, is an × -array, and no cell of contains a symbol that appears in the corresponding cell of , then there is a completion of that avoids ; that is, there is a Latin square that agrees with on every non-empty cell of , and, for each , satisfying 1 ≤ , ≤ , the symbol in position (, ) in does not appear in the corresponding cell of .

Journal of Combinatorial Designs, Volume 27, Issue 4, p. 229-250, doi.org/10.1002/jcd.21642 Abstract We have performed a complete enumeration of nonisotopic triples of mutually orthogonal Latin rectangle. Here we will present a census of such triples, classified by various properties, including the order of the autotopism group of the triple. As part of this, we have also achieved the first enumeration of pairwise orthogonal triples of Youden rectangles. We have also studied orthogonal triples of rectangles which are formed by extending mutually orthogonal triples with nontrivial autotopisms one row at a time, and requiring that the autotopism group is nontrivial in each step. This class includes a triple coming from the projective plane of order 8. Here we find a remarkably symmetrical pair of triples of rectangles, formed by juxtaposing two selected copies of complete sets of mutually orthogonal Latin squares of order 4.

Journal Version Physical Review E 99 Abstract A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find tha

Journal of Applied Probability Abstract Let V be an n-set, and let X be a random variable taking values in the power-set of V. Suppose we are given a sequence of random coupons , where the are independe

Journal of Graph Theory Abstract We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture

How to be an anti-capitalist for the 21st century

The American sociologist Erik Olin Wright was invited  to Stockholm for a talk in 2017 by the Institute for Futures Studies and Katalys. Moderator is Stefan Svallfors, and discussants are: Marika Lindg

Working papers 2022:1-11 Editor: Paul Bowman Proximity Principle, Adieu Robert E. Goodin Reconceiving the Democratic Boundary Problem David Miller The Boundary Problem and Platitudes About Democracy: A Conc

New year and new exciting projects! One of them is named Anxieties of Democracy, which will investigate in what ways representative democracy may be said to be in crisis, to explain why this is so, and