Star Critical Ramsey Numbers For Graphs
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Star-Critical Ramsey Numbers for Graphs
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.
Star-Critical Ramsey Numbers for Graphs
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.
Combinatorics, Graph Theory and Computing
This proceedings volume convenes selected, revised papers presented at the 52nd Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2021), virtually held at Florida Atlantic University in Boca Raton, USA, on March 8-12, 2021. As has been a tradition since its inception in 1970, this edition once more brought together mathematicians, practitioners, and scientists around novel findings in combinatorics, graph theory and computing, and their interactions. The lectures and works presented at the Conference have proven to be of great interest to other scientists and analysts employing these mathematical sciences in their professional activities in business, industry, and government. Such an environment promotes a better understanding of the roles of modern applied mathematics, combinatorics, and computer science. Many works have demonstrated that disciplines have increasingly contributed to each other. With this series of Conferences, the gaps between the fields tend to decrease even further. This volume is of particular interest for the community of pure and applied mathematicians in academia, industry, and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields. Its findings can also benefit a general audience of practitioners and students from related fields.