A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function
-
Published:2021-04-09
Issue:2
Volume:28
Page:
-
ISSN:1077-8926
-
Container-title:The Electronic Journal of Combinatorics
-
language:
-
Short-container-title:Electron. J. Combin.
Author:
Aliste-Prieto José,Crew Logan,Spirkl Sophie,Zamora José
Abstract
This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of XB and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted XB admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting XB to other graph functions. Second, we give several methods for constructing nonisomorphic graphs with equal chromatic and Tutte symmetric functions, and use them to provide specific examples.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Marked Graphs and the Chromatic Symmetric Function;SIAM Journal on Discrete Mathematics;2023-08-24
2. Plethysms of Chromatic and Tutte Symmetric Functions;The Electronic Journal of Combinatorics;2022-07-29
3. Modular relations of the Tutte symmetric function;Journal of Combinatorial Theory, Series A;2022-04
4. $H$-Chromatic Symmetric Functions;The Electronic Journal of Combinatorics;2022-02-11
5. A Complete Multipartite Basis for the Chromatic Symmetric Function;SIAM Journal on Discrete Mathematics;2021-01