Flip distances between graph orientations

Oswin Aichholzer, Jean Cardinal, Tony Huynh, Kolja Knauer, Torsten Mütze, Raphael Steiner, Birgit Vogtenhuber

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Abstract

Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. A natural computational problem to consider is the flip distance: Given two objects, what is the minimum number of flips needed to transform one into the other? We consider flip graphs on so-called $-orientations of a graph $G$, in which every vertex $v$ has a specified outdegree $v)$, and a flip consists of reversing all edges of a directed cycle. We prove that deciding whether the flip distance between two $-orientations of a planar graph $G$ is at most 2 is complete. This also holds in the special case of plane perfect matchings, where flips involve alternating cycles. We also consider the dual question of the flip distance between graph orientations in which every cycle has a specified number of forward edges, and a flip is the reversal of all edges in a minimal directed cut. In general, the problem remains hard, but if we only change sinks into sources, or vice-versa, then the problem can be solved in polynomial time.
Original languageEnglish
Title of host publication45th International Workshop on Graph-Theoretic Concepts in Computer Science
Place of PublicationVall de Nuria, Spain
Pages120-134
Number of pages15
Volume11789
Publication statusPublished - 2019

Publication series

NameLecture Notes in Computer Science (LNCS)

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Fields of Expertise

  • Information, Communication & Computing

Cite this

Aichholzer, O., Cardinal, J., Huynh, T., Knauer, K., Mütze, T., Steiner, R., & Vogtenhuber, B. (2019). Flip distances between graph orientations. In 45th International Workshop on Graph-Theoretic Concepts in Computer Science (Vol. 11789, pp. 120-134). (Lecture Notes in Computer Science (LNCS)). Vall de Nuria, Spain.