
TL;DR
This paper introduces sum-perfect graphs, a new class characterized by a specific inequality involving independence and clique numbers, and provides a forbidden subgraph characterization for these graphs.
Contribution
The paper defines sum-perfect graphs and establishes a forbidden induced subgraph characterization using a set of 27 graphs.
Findings
Sum-perfect graphs are characterized by 27 forbidden induced subgraphs.
A new class of graphs related to perfect graphs is introduced.
The characterization provides a basis for further structural and algorithmic studies.
Abstract
Inspired by a famous characterization of perfect graphs due to Lov\'{a}sz, we define a graph to be sum-perfect if for every induced subgraph of , . (Here and denote the stability number and clique number, respectively.) We give a set of graphs and we prove that a graph is sum-perfect if and only if does not contain any of the graphs in the set as an induced subgraph.
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.
