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<div class="csl-entry">Feller, R. M. (2024, July 31). <i>A complexity dichotomy for graph orientation problems</i> [Conference Presentation]. Midsummer Combinatorial Workshop XXIX, Prague, Czechia. https://doi.org/10.34726/8499</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/210539
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dc.identifier.uri
https://doi.org/10.34726/8499
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dc.description.abstract
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.
