On the Grundy number of Cameron graphs
Wing-Kai Hon, Ton Kloks, Fu-Hong Liu, Hsiang-Hsuan Liu, Tao-Ming, Wang
TL;DR
This paper proves that the Grundy number, representing the maximum colors in a first-fit coloring, can be computed efficiently in polynomial time specifically for Cameron graphs, a class derived from cographs via Seidel switching.
Contribution
It establishes the polynomial-time computability of the Grundy number for Cameron graphs, expanding understanding of coloring complexities in this graph class.
Findings
Grundy number is polynomial-time computable for Cameron graphs
Cameron graphs are the Seidel switching class of cographs
First-fit coloring reaches the Grundy number in Cameron graphs
Abstract
The Grundy number of a graph is the maximal number of colors attained by a first-fit coloring of the graph. The class of Cameron graphs is the Seidel switching class of cographs. In this paper we show that the Grundy number is computable in polynomial time for Cameron graphs.
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 · Interconnection Networks and Systems · graph theory and CDMA systems