9338

694 دكتري

دكتري

علوم رياضي- رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

هفت،97ص.

ص.ع.به فارسي و انگليسي

رياضي

ID694 دكتري

Ramsey Numbers of Loose Paths and Cycles in Uniform Hypergraphs Maryam Shahsiah m shahsiah@math iut ac ir September 22 2014 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Golamreza Omidi romidi@cc iut ac ir Advisor Dr Saeed Akbari s akbari@sharif ir Department Graduate Program Coordinator Dr Farid Bahrami fbahrami@cc iut ac it Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Abstract For given k uniform hypergraphs G and H the Ramsey number R G H is defined to be the smallest integer N so that in every red blue coloring of the edges of the complete k uniform is asymptotically 5 2 This result was extended by Gyarfas Sarkozy and Szemeredi to k hypergraph there is either a red copy of G or a blue copy of H Haxell et al proved that the 2 color Ramsey number of 3 uniform loose cycles on 2n vertices uniform loose cycles In this thesis we provide the exact values of 2 color Ramsey numbers involving loose paths and cycles in 3 uniform hypergraphs These give a positive answer to a question of Gyarfas and Raeisi In the sequel we conjecture that for every n m 3 and k 3 1 1 We show that how the truth of the last equality of the conjecture leads to the truth of the hole of conjecture We also demonstrate that for a fixed m 3 and k 4 if the conjecture holds for $m leq n leq 2m $ then it holds for all n m Subsequently the conjecture follows for m 3 In addition we study the Ramsey number of loose cycles in k uniform hypergraphs when k 4 5 and k 8 Keywords $k$ uniform hypergraph Ramsey number Loose path Loose cycle Mathematics Subject Classification 2012 05C65 05C55 05D10

غلامرضا اميدي

سعيد اكبري

بهروز طايفه رضايي،ابراهيم قرباني،بهناز عمومي