On general position sets in Cartesian productsKlavžar, Sandi (Avtor) Patkós, Balázs (Avtor) Rus, Gregor (Avtor) Yero, Ismael G. (Avtor) general position problemCartesian product of graphspaths and cyclesprobabilistic constructionsexact enumerationThe 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 gp-sets of G. The general position number of cylinders Pr ◻ Cs is deduced. It is proved that (Cr ◻ Cs)∈{6,7} whenever r ≥ s ≥ 3, s ≠ 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 ◻ Ps, where r,s ≥ 2, is also determined.Birkhäuser20212024-08-27 08:41:47Znanstveno delo90235sl