EAN: 9783031299803

SPRINGERBRIEFS IN MATHEMATICS STAR-CRITICAL R...

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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