Obstructions for acyclic local tournament orientation completions
Kevin Hsu, Jing Huang

TL;DR
This paper identifies minimal obstructions preventing the completion of partially oriented graphs to acyclic local tournaments, providing a polynomial-time recognition method for these obstructions.
Contribution
It introduces the first characterization of obstructions for acyclic local tournament orientation completions, enabling efficient recognition.
Findings
Obstructions are minimal partially oriented graphs that cannot be completed.
Obstructions can be recognized in polynomial time.
Results facilitate understanding of orientation completion problems for local tournaments.
Abstract
The orientation completion problem for a fixed class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class. Orientation completion problems have been studied recently for several classes of oriented graphs, yielding both polynomial time solutions and NP-completeness results. Local tournaments are a well-structured class of oriented graphs that generalize tournaments and their underlying graphs are intimately related to proper circular-arc graphs. Proper interval graphs are precisely those which can be oriented as acyclic local tournaments. It has been proved that the orientation completion problems for local tournaments and acyclic local tournaments are both polynomial time solvable. In this paper we identify the obstructions for acyclic local tournament orientation completions. These are in a sense minimal partially oriented…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Optimization and Search Problems
