Total difference chromatic numbers of regular infinite graphs

Benson-Tilsen, Noam; Brock, Samuel; Faunce, Brandon; Kumar, Monish; Stein, Noah Dokko; Zelinsky, Joshua

doi:10.2140/involve.2023.16.765

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-4184 (e-only)

ISSN: 1944-4176 (print)

Author Index

Coming Soon

Other MSP Journals

This article is available for purchase or by subscription. See below.

Total difference chromatic numbers of regular infinite graphs

Noam Benson-Tilsen, Samuel Brock, Brandon Faunce, Monish Kumar, Noah Dokko Stein and Joshua Zelinsky

Vol. 16 (2023), No. 5, 765–781

DOI: 10.2140/involve.2023.16.765

Abstract

Given a graph $G$ , a $k$ -total difference labeling of the graph is a total labeling $f$ from the set of edges and vertices to the set ${1, 2, \dots, k}$ satisfying $f ({u, v}) = | f (u) - f (v) |$ for any edge ${u, v}$ . If $G$ is a graph, then $χ_{td} (G)$ is the minimum $k$ such that there is a $k$ -total difference labeling of $G$ in which no two adjacent labels are identical. We extend prior work on total difference labeling by improving the upper bound on $χ_{td} (K_{n})$ and also by proving results concerning infinite regular graphs.

PDF Access Denied

We have not been able to recognize your IP address 3.138.181.145 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords

graph coloring, chromatic number

Mathematical Subject Classification

Primary: 05C15

Secondary: 05C63

Milestones

Received: 3 August 2021

Revised: 6 November 2022

Accepted: 13 November 2022

Published: 9 December 2023

Communicated by Kenneth S. Berenhaut

Authors

Noam Benson-Tilsen
Cornell University Ithaca, NY United States

Samuel Brock
Yale University New Haven, CT United States

Brandon Faunce
Rochester Institute of Technology Rochester, NY United States

Monish Kumar
Hopkins School New Haven, CT United States

Noah Dokko Stein
Yale University New Haven, CT United States

Joshua Zelinsky
Hopkins School New Haven, CT United States

Vol. 16, No. 5, 2023