Minimum coprime graph labelings
Catherine Lee

TL;DR
This paper investigates the minimum coprime number for various graph classes, providing exact values, resolving conjectures, and analyzing asymptotic behavior for random graphs.
Contribution
It determines the minimum coprime number for specific graph classes, resolves existing conjectures, and offers asymptotic results for Erdős-Rényi random graphs.
Findings
Exact minimum coprime numbers for certain graph classes
Resolution of three conjectures in the literature
Asymptotic behavior for Erdős-Rényi random graphs
Abstract
A coprime labeling of a graph is a labeling of the vertices of with distinct integers from to such that adjacent vertices have coprime labels. The minimum coprime number of is the least for which such a labeling exists. In this paper, we determine the minimum coprime number for several well-studied classes of graphs, including the coronas of complete graphs with empty graphs and the joins of two paths. In particular, we resolve a conjecture of Seoud, El Sonbaty, and Mahran and two conjectures of Asplund and Fox. We also provide an asymptotic for the minimum coprime number of the Erd\H{o}s-R\'enyi random graph.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph Labeling and Dimension Problems · Limits and Structures in Graph Theory · graph theory and CDMA systems
