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Star-critical Ramsey numbers for graphs

Budden, Mark R.

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Star-critical Ramsey numbers for graphs

Record Type:	Electronic resources : Monograph/item
Title/Author:	Star-critical Ramsey numbers for graphs/ by Mark R. Budden.
Author:	Budden, Mark R.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	1 online resource (xiii, 92 p.) :ill., digital ;24 cm.
[NT 15003449]:	1. Multi Star-Critical Ramsey Numbers -- 2. Non-Complete Graphs -- 3. Generalizations of Star-Critical Ramsey Numbers -- 4. Open Problems.
Contained By:	Springer Nature eBook
Subject:	Ramsey numbers. -
Online resource:	https://doi.org/10.1007/978-3-031-29981-0
ISBN:	9783031299810

Star-critical Ramsey numbers for graphs
Budden, Mark R.

Star-critical Ramsey numbers for graphs[electronic resource] /by Mark R. Budden. - Cham :Springer International Publishing :2023. - 1 online resource (xiii, 92 p.) :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

1. Multi Star-Critical Ramsey Numbers -- 2. Non-Complete Graphs -- 3. Generalizations of Star-Critical Ramsey Numbers -- 4. Open Problems.

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.

ISBN: 9783031299810

Standard No.: 10.1007/978-3-031-29981-0doiSubjects--Topical Terms:

3634487
Ramsey numbers.

LC Class. No.: QA166

Dewey Class. No.: 511.5

Star-critical Ramsey numbers for graphs
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520 $a 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.
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