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On some extremal position problems for graphsJames Tuite,
Elias John Thomas,
Ullas Chandran S.V., 2025, original scientific article
Abstract: The general position number of a graph G is the size of the largest set of vertices S such that no geodesic of G contains more than two elements of S. The monophonic position number of a graph is defined similarly, but with `induced path' in place of `geodesic'. In this paper we investigate some extremal problems for these parameters. Firstly we discuss the problem of the smallest possible order of a graph with given general and monophonic position numbers. We then determine the asymptotic order of the largest size of a graph with given general or monophonic position number, classifying the extremal graphs with monophonic position number two. Finally we establish the possible diameters of graphs with given order and monophonic position number.
Keywords: general position, monophonic position, Turán problems, size, diameter, induced path
Published in RUP: 21.10.2025; Views: 526; Downloads: 3
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