On oriented cliques with respect to push operation

Article Type

Research Article

Publication Title

Discrete Applied Mathematics

Abstract

An oriented graph is a directed graph without any directed cycle of length at most 2. An oriented clique is an oriented graph whose non-adjacent vertices are connected by a directed 2-path. To push a vertex v of an oriented graph is to change the orientations of all the arcs incident to v. A push clique is an oriented clique that remains an oriented clique even if one pushes any set of vertices of it. We show that it is NP-complete to decide if an undirected graph is the underlying graph of a push clique or not. We also prove that a planar push clique can have at most 8 vertices and provide an exhaustive list of planar push cliques.

First Page

50

Last Page

63

DOI

10.1016/j.dam.2017.07.037

Publication Date

12-11-2017

Comments

Open Access, Bronze, Green

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