# Research

## Open problems

Here is the list of open problems from the Workshop on Valued Constraint Satisfaction Problems in Krakow, Jan 19–23, 2015. Some of them are already solved.## Papers

**On the complexity of H-coloring for special oriented trees**, to appear in European Journal of Combinatorics (2017) arXiv:1407.1779**Deciding absorption in relational structures**with L. Barto, to appear in Algebra Universalis (2016) arXiv:1601.06450**A finer reduction of constraint problems to digraphs**with D. Delić, M. Jackson and T. Niven, Logical Methods in Computer Science 11(4:18) (2015), 1–33. arXiv:1406.6413**Decidability of absorption in relational structures of bounded width**, Algebra Universalis 72/1 (2014), 15–28. PDF**CSP dichotomy for special polyads**with L. Barto, Int. J. Algebra Comput. 23/05 (2013), 1151–1174. PDF (doi:10.1142/S0218196713500215 © 2013 World Scientific Publishing Company)**On the reduction of the CSP dichotomy conjecture to digraphs**with D. Delić, M. Jackson and T. Niven, 19th Int. Conf. on Principles and Practice of Constraint Programming, LNCS 8124 (2013), 184–199. arXiv:1305.2039

## Theses

**Constraint satisfaction, graphs and algebras**, PhD thesis, Charles University in Prague, 2014. PDF**The algebraic approach to CSP**, Master's thesis, Charles University in Prague, 2010. PDF**Selected topics from Tame Congruence Theory**, Bachelor's thesis, Charles University in Prague, 2008. PDF

## Conference talks

**Clonoids and Promise CSP**, AAA94+NSAC 2017, Novi Sad 2017.**On the subpower membership problem**, The 52nd Summer School on General Algebra and Ordered Sets (SSAOS), Stará Lesná 2014. (PDF)**Algebraic approach to coloring by oriented trees**, The 4th Novi Sad Algebraic Conference (NSAC), Novi Sad 2013. (PDF)**Reduction of the CSP dichotomy conjecture to digraphs**, The 51st Summer School on General Algebra and Ordered Sets (SSAOS), Trojanovice 2013. (PDF)**CSP dichotomy for special oriented trees**, The 83rd Workshop on General Algebra (AAA), Novi Sad 2012. (PDF)**Algebraic reduction of CSP to digraphs**, Conference on Universal Algebra and Lattice Theory, Szeged 2012. (PDF)**Absorption in finitely related SD(meet) algebras has bounded arity**, Workshop on Algebra and CSPs, Toronto 2011. (PDF)**CSP and oriented trees**, The 79th Workshop on General Algebra (AAA), Olomouc 2010. (PDF)**CSP dichotomy for special polyads**, The 3rd Novi Sad Algebraic Conference (NSAC), Novi Sad 2009. (PDF)

## Seminar talks

**Finer complexity classification of CSPs**, Warsaw University of Technology, December 2014.**Subpower membership problem**, Warsaw University of Technology, November 2013.**Algebraic approach to coloring by oriented trees**, Algebra seminar, Johannes Kepler University, Linz 2013.**Absorption in relational structures**, Algebra seminar, Johannes Kepler University, Linz 2012.**Algebraic approach to CSP and oriented trees**, Algebra seminar, La Trobe University, Melbourne 2012.**Polymorphisms of special trees**, Visitor's seminar, Fields Institute for Research in Mathematical Sciences, Toronto 2011.**CSP dichotomy for special polyads**, Algebra Seminar, University of Szeged, Szeged 2009.