Chromatic Symmetric Functions of Conjoined Graphs

Ethan Yuanjian Qi; Davion Qibao Tang; David G.L. Wang

doi:10.1007/s11464-024-0088-3

Chromatic Symmetric Functions of Conjoined Graphs

Ethan Yuanjian Qi
, Davion Qibao Tang
, David G.L. Wang^*

^*Corresponding author for this work

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	139-166
Number of pages	28
Journal	Frontiers of Mathematics
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s11464-024-0088-3
Publication status	Published - Jan 2026
Externally published	Yes

Keywords

05A15
05E05
Chromatic symmetric function
Stanley–Stembridge’s conjecture
conjoined graph
e-positivity

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10.1007/s11464-024-0088-3

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title = "Chromatic Symmetric Functions of Conjoined Graphs",

abstract = "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 eI-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.",

keywords = "05A15, 05E05, Chromatic symmetric function, Stanley–Stembridge{\textquoteright}s conjecture, conjoined graph, e-positivity",

author = "Qi, \{Ethan Yuanjian\} and Tang, \{Davion Qibao\} and Wang, \{David G.L.\}",

note = "Publisher Copyright: {\textcopyright} Peking University 2025.",

year = "2026",

month = jan,

doi = "10.1007/s11464-024-0088-3",

language = "English",

volume = "21",

pages = "139--166",

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TY - JOUR

T1 - Chromatic Symmetric Functions of Conjoined Graphs

AU - Qi, Ethan Yuanjian

AU - Tang, Davion Qibao

AU - Wang, David G.L.

N1 - Publisher Copyright: © Peking University 2025.

PY - 2026/1

Y1 - 2026/1

N2 - 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 eI-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.

AB - 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 eI-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.

KW - 05A15

KW - 05E05

KW - Chromatic symmetric function

KW - Stanley–Stembridge’s conjecture

KW - conjoined graph

KW - e-positivity

UR - https://www.scopus.com/pages/publications/105021450624

U2 - 10.1007/s11464-024-0088-3

DO - 10.1007/s11464-024-0088-3

M3 - Article

AN - SCOPUS:105021450624

SN - 2731-8648

VL - 21

SP - 139

EP - 166

JO - Frontiers of Mathematics

JF - Frontiers of Mathematics

IS - 1

ER -

Chromatic Symmetric Functions of Conjoined Graphs

Abstract

Keywords

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