Abstract:A subset S of vertices of a graph G is a general position set if no shortest path in G contains three or more vertices of S. In this paper, we generalise a problem of M. Gardner to graph theory by introducing the lower general position number gp − (G) of G, which is the number of vertices in a smallest maximal general position set of G. We show that gp − (G) = 2 if and only if G contains a universal line and determine this number for several classes 2 Di Stefano, Klavžar, Krishnakumar, Tuite and Yero of graphs… Show more
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