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arXiv · 1903.04286

The general position problem on Kneser graphs and on some graph operations

Modjtaba Ghorbani·Sandi Klavžar·Hamid Reza Maimani·Mostafa Momeni·Farhad Rahimi Mahid·Gregor Rus
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Abstract

A vertex subset $S$ of a graph $G$ is a general position set of $G$ if no vertex of $S$ lies on a geodesic between two other vertices of $S$. The cardinality of a largest general position set of $G$ is the general position number (gp-number) ${\rm gp}(G)$ of $G$. The gp-number is determined for some families of Kneser graphs, in particular for $K(n,2)$ and $K(n,3)$. A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.

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Modjtaba Ghorbani, Sandi Klavžar, Hamid Reza Maimani, Mostafa Momeni, Farhad Rahimi Mahid, Gregor Rus. 2019-03-11. The general position problem on Kneser graphs and on some graph operations. https://arxiv.org/abs/1903.04286

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