Chromatic symmetric functions of conjoined graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910009112133632 |
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| author | Qi, E. Y. J. Tang, D. Q. B. Wang, D. G. L. |
| author_facet | Qi, E. Y. J. Tang, D. Q. B. Wang, D. G. L. |
| contents | We introduce path-conjoined graphs defined for two rooted graphs by joining their roots with a path, and investigate the chromatic symmetric functions of its two generalizations: spider-conjoined graphs and chain-conjoined graphs. By using the composition method developed by Zhou and the third author recently, we obtain neat positive $e_I$-expansions for the chromatic symmetric functions of clique-path-cycle graphs, path-clique-path graphs, and clique-clique-path graphs. We pose the $e$-positivity conjecture for hat-chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01418 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chromatic symmetric functions of conjoined graphs Qi, E. Y. J. Tang, D. Q. B. Wang, D. G. L. Combinatorics 05E05, 05A15 We introduce path-conjoined graphs defined for two rooted graphs by joining their roots with a path, and investigate the chromatic symmetric functions of its two generalizations: spider-conjoined graphs and chain-conjoined graphs. By using the composition method developed by Zhou and the third author recently, we obtain neat positive $e_I$-expansions for the chromatic symmetric functions of clique-path-cycle graphs, path-clique-path graphs, and clique-clique-path graphs. We pose the $e$-positivity conjecture for hat-chains. |
| title | Chromatic symmetric functions of conjoined graphs |
| topic | Combinatorics 05E05, 05A15 |
| url | https://arxiv.org/abs/2406.01418 |