2015/11/27 by Bensmail, Julien, Nandi, Soumen, Sen, Sagnik · 1 citation
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1511.08672
To push a vertex v of a directed graph \overrightarrowG is to change the orientations of all the arcs incident with v. An oriented graph is a directed graph without any cycle of length at most 2. An oriented clique is an oriented graph whose non-adjacent vertices are connected by a directed 2-path. 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 underlying graph of a push clique or not. We also prove that a planar push clique can have at most 8 vertices. We also provide an exhaustive list of minimal (with respect to spanning subgraph inclusion) planar push cliques.