Rainbow Graphs and Switching Classes
Suho Oh, Hwanchul Yoo, Taedong Yun

TL;DR
This paper explores the properties of rainbow graphs, a special class of vertex-colored graphs, and establishes a bijection between rainbow graphs on 2n vertices and switching classes of graphs on n vertices, revealing a deep combinatorial connection.
Contribution
It introduces a novel bijection linking rainbow graphs and switching classes, advancing understanding of their structural relationship.
Findings
Established a bijection between n-rainbow graphs on 2n vertices and switching classes on n vertices.
Provided insights into the structural properties of rainbow graphs.
Connected rainbow graphs to graph switching classes, enriching combinatorial graph theory.
Abstract
A rainbow graph is a graph that admits a vertex-coloring such that every color appears exactly once in the neighborhood of each vertex. We investigate some properties of rainbow graphs. In particular, we show that there is a bijection between the isomorphism classes of n-rainbow graphs on 2n vertices and the switching classes of graphs on n vertices.
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
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems
