A deletion–contraction relation for the chromatic symmetric function. (October 2020)

• Record Type: Journal Article
• Authors: Crew, Logan; Spirkl, Sophie
• Is Part Of: European journal of combinatorics. Volume 89(2020)
• Publication Date: 2020-10
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2020.103143
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We extend the definition of the chromatic symmetric function X G to include graphs G with a vertex-weight function w : V ( G ) → N . We show how this provides the chromatic symmetric function with a natural deletion–contraction relation analogous to that of the chromatic polynomial. Using this relation we derive new properties of the chromatic symmetric function, and we give alternate proofs of many fundamental properties of X G .