Séminaire Lotharingien de Combinatoire, 95B.4 (2026), 12 pp.
Ron M. Adin, Sergi Elizalde, Pál Hegedüs, and Yuval Roichman
The Chromatic Symmetric Function of Graphs Glued at a Single Vertex
Abstract.
We describe how the chromatic symmetric function of two graphs glued
at a single vertex can be expressed as a matrix multiplication using
certain information of the two individual graphs. We then prove
new e-positivity results by using a connection between forest
triples, defined by the first author, and Hikita's probabilities
associated to standard Young tableaux. Specifically, we prove that
gluing a sequence of unit interval graphs and cycles results in
an e-positive graph. We also prove e-positivity for a
graph obtained by gluing the first and last vertices of such a
sequence. This generalizes e-positivity of cycle-chord graphs
and supports Ellzey's conjectured e-positivity for proper
circular arc digraphs.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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