Logan Crew

activity

20182026

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Showing math.COShow all

5 papers · 1 filter

math.CO2026

Characterizing Large Clique Number in Tournaments

Logan Crew, Xinyue Fan, Hidde Koerts +2

Aboulker, Aubian, Charbit, and Lopes (2023) defined the clique number of a tournament to be the minimum clique number of one of its backedge graphs. Here we show that if $T$ is a t…

math.CO2022

Homogeneous Sets in Graphs and a Chromatic Multisymmetric Function

Logan Crew, Evan Haithcock, Josephine Reynes +1

In this paper, we extend the chromatic symmetric function $X$ to a chromatic $k$ -multisymmetric function $X_{k}$ , defined for graphs equipped with a partition of their vertex set int…

math.CO2021

A Note on Distinguishing Trees with the Chromatic Symmetric Function

Logan Crew

For a tree $T$ , consider its smallest subtree $T^{\circ}$ containing all vertices of degree at least $3$ . Then the remaining edges of $T$ lie on disjoint paths each with one endpoi…

math.CO2019

A Deletion-Contraction Relation for the Chromatic Symmetric Function

Logan Crew, Sophie Spirkl

We extend the definition of the chromatic symmetric function $X_{G}$ to include graphs $G$ with a vertex-weight function $w : V (G) \to N$ . We show how this provides…

math.CO2019

Disproportionate division

Logan Crew, Bhargav Narayanan, Sophie Spirkl

We study the disproportionate version of the classical cake-cutting problem: how efficiently can we divide a cake, here $[0, 1]$ , among $n$ agents with different demands $α_1, α_2,…