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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| Summary: | 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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| ISSN: | 0195-6698 |
| DOI: | 10.1016/j.ejc.2020.103143 |