Some Position Problems for Graphs

Tuite, James; Thomas, Elias John and Chandran S. V., Ullas (2022). Some Position Problems for Graphs. In: Algorithms and Discrete Applied Mathematics: 8th International Conference, CALDAM 2022, 10-12 Feb 2022, Puducherry, India, pp. 36–47.



The general position problem for graphs stems from a puzzle of Dudeney and the general position problem from discrete geometry. 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 abstract we discuss the smallest possible order of a graph with given general and monophonic position numbers, determine the asymptotic order of the largest size of a graph with given order and position numbers and finally determine the possible diameters of a graph with given order and monophonic position number.

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