Graph orientation problems with forbidden tournaments
Given a finite set of oriented graphs F, the F-free orientation problem is the following decision problem. Given a finite input graph, is there an orientation of its edges such that the resulting directed graph omits every member of F. If the set F consists of tournaments (i.e. complete oriented graphs), Bodirsky and Guzmán-Pro have recently established that this computational problem exhibits a complexity dichotomy: it is either solvable in polynomial time or NP-complete. I will explain how the F-free orientation problem can be viewed as the constraint satisfaction problem (CSP) of an omega-categorical template, making it amenable to universal algebraic methods. In particular I will demonstrate how the recently developed technique of "smooth approximations", provides a shorter algebraic proof of the complexity dichotomy for the graph orientation problem.
Publication Details
- Journal
- reposiTUm (TU Wien)
- Published
- 2024-10-15
- DOI
- https://doi.org/10.34726/8500
- Primary Topic
- Plant Ecology and Soil Science
- Type
- article
- Field-Weighted Citation Impact
- 0.00