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＜電子ブック＞
Star-Critical Ramsey Numbers for Graphs / by Mark R. Budden
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XIII, 92 p. 43 illus., 42 illus. in color : online resource
著者標目	*Budden, Mark R author SpringerLink (Online service)
件　名	LCSH:Graph theory FREE:Graph Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-29981-0

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