Regular Turán numbers and some Gan–Loh–Sudakov‐type problems. Issue 1 (18th July 2022)

• Record Type: Journal Article
• Authors: Cambie, Stijn; de Joannis de Verclos, Rémi; Kang, Ross J.
• Is Part Of: Journal of graph theory. Volume 102:Issue 1(2023)
• Page Start: 67
• Page End: 85
• Publication Date: 2022-07-18
• Subjects: cliques -- Gan‐Loh‐Sudakov‐type problem -- order -- regular graph -- size -- Turán number; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22857
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: Motivated by a Gan–Loh–Sudakov‐type problem, we introduce the regular Turán numbers, a natural variation on the classical Turán numbers where we restrict ourselves to the class of regular graphs. Among other results, we prove a striking supersaturation version of Mantel's theorem in the case of a regular host graph of odd order. We also characterize the graphs for which the regular Turán numbers behave classically or otherwise.