A deletion–contraction relation for the chromatic symmetric function
We extend the definition of the chromatic symmetric function XG 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 de...
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| Published in | European journal of combinatorics Vol. 89; p. 103143 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.10.2020
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| Online Access | Get full text |
| ISSN | 0195-6698 |
| DOI | 10.1016/j.ejc.2020.103143 |
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| Abstract | We extend the definition of the chromatic symmetric function XG 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 XG. |
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| AbstractList | We extend the definition of the chromatic symmetric function XG 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 XG. |
| ArticleNumber | 103143 |
| Author | Spirkl, Sophie Crew, Logan |
| Author_xml | – sequence: 1 givenname: Logan surname: Crew fullname: Crew, Logan email: crewl@math.upenn.edu organization: Department of Mathematics, University of Pennsylvania, Philadelphia, PA, United States of America – sequence: 2 givenname: Sophie orcidid: 0000-0002-2536-5618 surname: Spirkl fullname: Spirkl, Sophie email: sspirkl@math.princeton.edu organization: Department of Mathematics, Princeton University, Princeton, NJ, United States of America |
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| Cites_doi | 10.1006/aima.1995.1020 10.1016/0012-365X(92)90040-M 10.1016/j.disc.2016.09.019 10.1016/0012-365X(73)90108-8 10.1023/A:1011258714032 10.5802/aif.1706 10.1016/j.disc.2013.12.006 10.1016/j.aim.2015.12.018 10.37236/6660 10.1016/S0012-365X(98)00146-0 10.1016/S0012-365X(96)83014-7 10.1016/j.disc.2018.09.001 10.1006/aima.1996.0018 10.1016/S0012-365X(96)00245-2 10.1137/17M1144805 |
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