Overview
- Contains a list of open problems
- Includes all currently known results on star-critical Ramsey numbers
- Streamlines and simplifies proofs from their original sources
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (4 chapters)
Keywords
About this book
This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists.
This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges.
The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.
Authors and Affiliations
About the author
Mark Budden: Originally born in Baton Rouge, Louisiana, Mark Budden earned his Ph.D. in Mathematics from the University of Missouri-Columbia in 2003. From 2003-2010, he worked as a faculty member in the Department of Mathematics at Armstrong Atlantic State University (now Georgia Southern University’s Armstrong campus) in Savannah, Georgia. In 2010, he joined the faculty at Western Carolina University in Cullowhee, North Carolina, where he is now a Professor in the Department of Mathematics and Computer Science. Mark’s research interests span many topics in graph theory and number theory, and he places special emphasis on engaging undergraduate students in research projects.
Bibliographic Information
Book Title: Star-Critical Ramsey Numbers for Graphs
Authors: Mark R. Budden
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-031-29981-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Softcover ISBN: 978-3-031-29980-3Published: 14 May 2023
eBook ISBN: 978-3-031-29981-0Published: 13 May 2023
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIII, 92
Number of Illustrations: 1 b/w illustrations, 42 illustrations in colour
Topics: Graph Theory