Star-Critical Ramsey Numbers for Graphs

Mark R. Budden

ISBN 10: 3031299809 / ISBN 13: 9783031299803

Edité par Springer International Publishing, Springer Nature Switzerland Mai 2023, 2023

A propos de cet article

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 108 pp. Englisch.

N° de réf. du vendeur 9783031299803

Détails bibliographiques

• Titre: Star-Critical Ramsey Numbers for Graphs
• Éditeur: Springer International Publishing, Springer Nature Switzerland Mai 2023
• Date de parution: 2023
• Langue: anglais
• ISBN à 10 chiffres: 3031299809
• ISBN à 13 chiffres: 9783031299803
• Reliure: Taschenbuch
• État de l'article: Neu

A propos de ce titre

Synopsis

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.

À propos de l?auteur

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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.