Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
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.
On fan-saturated graphs

Jessica Fuller and Ronald J. Gould

Vol. 16 (2023), No. 4, 637–657

Given a graph H, we say that a graph G is H-saturated if it does not contain H as a subgraph, but the addition of any edge eE(G) would result in at least one copy of H as a subgraph. Let Ft be the graph consisting of t edge-disjoint triangles that intersect at a single vertex v. We investigate the set of all m such that there exists an n-vertex, m-edge Ft-saturated graph for t 2. This set is called the saturation spectrum of Ft. For example, there exists an F2-saturated graph G on n 10 vertices and m edges if m = n + 2, or

2n 3 m n + 5 2 n 5 2 + 3n 5 2 + 4,

or m = p(n p) + 1, the size of the complete bipartite graph with one additional edge, or m = n24 n x2 + 1, x 1.

PDF Access Denied

We have not been able to recognize your IP address 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
or by using our contact form.

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

fan, saturation, saturation spectrum
Mathematical Subject Classification
Primary: 05C35
Received: 17 May 2022
Revised: 3 October 2022
Accepted: 6 October 2022
Published: 31 October 2023

Communicated by Ann N. Trenk
Jessica Fuller
Department of Mathematics
University of Connecticut
Stamford, CT
United States
Ronald J. Gould
Department of Mathematics and Computer Science
Emory University
Atlanta, GA
United States