Bounding the number of cycles in a graph in terms of its degree sequence. (January 2021)

• Record Type: Journal Article
• Authors: Dvořák, Zdeněk; Morrison, Natasha; Noel, Jonathan A.; Norin, Sergey; Postle, Luke
• Is Part Of: European journal of combinatorics. Volume 91(2021)
• Publication Date: 2021-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2020.103206
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Király (2009) and Arman and Tsaturian (2017) and to improve upper bounds on the maximum number of cycles in a planar graph.