Ramsey-Tur\'an numbers for intersecting odd cliques
Min Liu

TL;DR
This paper determines the asymptotic maximum number of edges in large graphs avoiding certain intersecting odd cliques and independent sets, extending classical Ramsey-Turán results to more complex graph structures.
Contribution
It extends the classical Ramsey-Turán theorem to graphs containing multiple intersecting odd cliques sharing a vertex, showing they have similar edge bounds as single odd cliques.
Findings
The maximum edges in graphs avoiding intersecting odd cliques match classical bounds.
The results generalize Erdős and Sós's 1969 theorem.
Asymptotic edge bounds are established for complex clique structures.
Abstract
Given a graph and a function , the Ramsey-Tur\'an number of and , denoted by , is the maximum number of edges a graph on vertices can have, which does not contain as a subgraph and also does not contain a set of independent vertices. Let be a positive integer. In 1969, Erd\H{o}s and S\'os proved that . Let denote the graph consisting of copies of complete graphs sharing exactly one vertex. In this paper, we show that , which is of the same magnitude with .
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
TopicsComputability, Logic, AI Algorithms · Commutative Algebra and Its Applications · Limits and Structures in Graph Theory
