The Classification of Critical Graphs and Star-critical Ramsey Numbers
Author | : Jonelle Hook |
Publisher | : |
Total Pages | : 110 |
Release | : 2010 |
ISBN-10 | : 1109781512 |
ISBN-13 | : 9781109781519 |
Rating | : 4/5 (12 Downloads) |
Download or read book The Classification of Critical Graphs and Star-critical Ramsey Numbers written by Jonelle Hook and published by . This book was released on 2010 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The graph Ramsey number R(G,H) is the smallest integer n such that every 2-coloring of the edges of Kn contains either a red copy of G or a blue copy of H. This implies that there exists a critical graph, a 2-coloring of Kn -1 that does not contain a red copy of G or a blue copy of H. These facts propose a question. What is the largest star K1,k that can be removed from Kn so that the underlying graph is still forced to have either a red copy of G or a blue copy of H? That is, determine the smallest integer k such that every 2-coloring of Kn - K1,n-2- k has either a red G or a blue H and there exists a 2-coloring of Kn - K1,n-2- k without a red G or a blue H. We have determined this integer for various classes of graphs G and H where R(G,H) is known. In addition to finding star-critical Ramsey numbers, we have also classified the critical graphs for various graph Ramsey numbers.