LIPIcs.SWAT.2024.13.pdf
- Filesize: 0.8 MB
- 13 pages
An independent set in a graph is a set of vertices where no two vertices are adjacent to each other. A maximum independent set is the largest possible independent set that can be formed within a given graph G. The cardinality of this set is referred to as the independence number of G. This paper investigates the independence number of 1-planar graphs, a subclass of graphs defined by drawings in the Euclidean plane where each edge can have at most one crossing point. Borodin establishes a tight upper bound of six for the chromatic number of every 1-planar graph G, leading to a corresponding lower bound of n/6 for the independence number, where n is the number of vertices of G. In contrast, the upper bound for the independence number in 1-planar graphs is less studied. This paper addresses this gap by presenting upper bounds based on the minimum degree δ. A comprehensive table summarizes these upper bounds for various δ values, providing insights into achievable independence numbers under different conditions.
Feedback for Dagstuhl Publishing