TRAVERSING A GRAPH IN GENERAL POSITION
Sandi Klavžar, Aditi Krishnakumar, James Tuite, Ismael G. Yero · Bulletin of the Australian Mathematical Society · 2023
Abstract LetGbe a graph. Assume that to each vertex of a set of vertices $S\subseteq V(G)$ a robot is assigned. At each stage one robot can move to a neighbouring vertex. ThenSis a mobile general position set ofGif there exists a sequence of moves of the robots such that all the vertices ofGare visited while maintaining the general position property at all times. The mobile general position number ofGis the cardinality of a largest mobile general position set ofG. We give bounds on the mobile general position number and determine exact values for certain common classes of graphs, including block graphs, rooted products, unicyclic graphs, Kneser graphs $K(n,2)$ and line graphs of complete graphs.