03150nam 22005895 450 991072508820332120240320120729.09783031299810(electronic bk.)978303129980310.1007/978-3-031-29981-0(MiAaPQ)EBC7248879(Au-PeEL)EBL7248879(OCoLC)1379438632(DE-He213)978-3-031-29981-0(BIP)089067634(PPN)270614567(CKB)26637861200041(EXLCZ)992663786120004120230513d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierStar-Critical Ramsey Numbers for Graphs /by Mark R. Budden1st ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (102 pages)SpringerBriefs in Mathematics,2191-8201Print version: Budden, Mark R. Star-Critical Ramsey Numbers for Graphs Cham : Springer International Publishing AG,c2023 9783031299803 Includes bibliographical references and index.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.SpringerBriefs in Mathematics,2191-8201Graph theoryGraph TheoryTeoria de RamseythubTeoria de grafsthubLlibres electrònicsthubMathematicsGraph theory.Graph Theory.Teoria de RamseyTeoria de grafs511.5Budden Mark R.1358337MiAaPQMiAaPQMiAaPQ9910725088203321Star-Critical Ramsey Numbers for Graphs3367524UNINA