Ars Mathematica Contemporanea· 2026Q2
The general position problem: a survey
- 6citations
- Q2SCImago
- 2026year
Short summary
A survey of the general position problem in graph theory, which seeks the largest set of vertices where no three lie on a common shortest path, reveals extensive literature and diverse variations.
AI-generated from the title and abstract; the full text is not read.
Key points
- The general position problem asks for the largest vertex set S where no three vertices in S share a common shortest path.
- The paper surveys exact results for this problem across different graph classes.
- It examines how the general position number changes with graph products and operations.
- Variations of the problem, including those based on different graph convexities and dynamic, fractional, coloring, and game versions, are discussed.
AI-generated from the title and abstract; the full text is not read.
Abstract
Inspired by a chessboard puzzle of Dudeney, the general position problem in graph theory asks for a largest set S of vertices in a graph such that no three elements of S lie on a common shortest path. The number of vertices in such a largest set is the general position number of the graph. This paper provides a survey of this rapidly growing problem, which now has an extensive literature. We cover exact results for various graph classes and the behaviour of the general position number under graph products and operations. We also discuss interesting variations of the general position problem, including those corresponding to different graph convexities, as well as dynamic, fractional, colouring and game versions of the problem.
The authors' abstract, as published at the source. Ars Mathematica Contemporanea, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science