%0 Journal Article 
%A Klavžar, Sandi
%A Patkós, Balázs
%A Rus, Gregor
%A González Yero, Ismael
%T On General Position Sets in Cartesian Products
%D 2021
%@ 1422-6383

%U http://hdl.handle.net/10498/26516
%X The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gpsets of G. The general position number of cylinders Pr square Cs is deduced. It is proved that gp(Cr square C-s). {6, 7} whenever r >= s = 3, s >=not equal 4, and r >= 6. A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in Pr square Ps, where r, s >= 2, is also determined.
%K General position problem
%K Cartesian product of graphs
%K paths and cycles
%K probabilistic constructions
%K exact enumeration
%~ Universidad de Cádiz