7292

6798

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

هشت، 61ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

غلامرضا اميدي

بهناز عمومي

24/8/91

سعيد اكبري، ابراهيم قرباني

1396/09/21

كتابنامه

علوم رياضي

رياضي

ID6798

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

On Diagonal Ramsey Numbers of Graphs and Hypergraphs Leila Maherani l maherani@math iut ac ir 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Gholam Reza Omidi romidi@cc iut ac ir Advisor Dr Behnaz Omoomi bomoomi@cc iut ac ir 2010 MSC 05D10 05C65 Keywords Ramsey number Diagonal Ramsey number Ramsey linear family Abstract In this thesis we study the diagonal Ramsey numbers of particular classes of graphs and hyper graphs For given graphs G1 G2 Gk the k color Ramsey number r G1 G2 Gk is the leastpositive integer n such that for every k coloring of the edges of the complete graph Kn with distinctcolors 1 2 k there is a monochromatic copy of Gi in color i for some 1 i k Determining orestimating Ramsey numbers is one of the central problem in Combinatorics A problem on Ramseynumbers of general graphs was posed in 1983 by Erd s and Graham They conjectured that among all graphs with m n edges and no isolated vertices the complete graph on n vertices has the 2largest Ramsey number On the other hand one of the oldest results in Ramsey theory proved byErd s and Szekeres in 1935 asserts that the Ramsey number of the complete graph with m edges is at most 2O m Since the number of vertices in the complete graph with m edges is approximately a constant multiple of m Erd s conjectured that there is a constant c such that r G 2c m forevery graph G with m edges and no isolated vertices In 2011 Sudakove proved this conjecture Here we present the Sudukov s result and then give anextension of his result

غلامرضا اميدي

بهناز عمومي

سعيد اكبري، ابراهيم قرباني