Coloring problem of signed interval graphs
F. Ramezani
TL;DR
This paper investigates the coloring and clique problems for signed interval graphs, establishing NP-completeness for coloring while showing the clique problem remains polynomial-time solvable.
Contribution
It proves that coloring signed interval graphs is NP-complete, contrasting with the polynomial-time solvability of their clique problem, and explores related complexities.
Findings
Coloring problem of signed interval graphs is NP-complete.
Clique problem of signed interval graphs is in P.
Further related problems are also analyzed for complexity.
Abstract
The chromatic number of signed graphs is defined recently. The coloring and clique problem of interval graphs has been studied and polynomial time algorithms are established. Here we consider these problems for signed interval graphs and prove that the coloring problem of signed interval graphs is NP-complete whereas their ordinary clique problem is in P. We also study the complexity of further related problems.
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 · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems