پديد آورنده :
رئيسي، غفار
عنوان :
اعداد رمزي گراف ها و ابر گراف ها
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
73ص.: مصور،جدول،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
غلامرضا اميدي
استاد مشاور :
بهناز عمومي
توصيفگر ها :
05C65 , 05C55 , 05C15
تاريخ نمايه سازي :
1/8/91
استاد داور :
سعيد اكبري، ابراهيم قرباني، جواد باقريان
كد ايرانداك :
ID453 دكتري
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
On Ramsey Number of Graphs and Hypergraphs Ghaffar Raeisi g raeisi@math iut ac ir April 30 2012 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Gholam Reza Omidi romidi@cc iut ac ir Advisor Dr Behnaz Omoomi bomoomi@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Abstract Let H1 H2 Ht be arbitrary k uniform hypergraphs The hypergraph Ramsey numberR H1 H2 Ht is the smallest integer N such that in every t coloring of the hyperedges of kthe complete k uniform hypergraph KN there is a monochromatic copy of Hi in color i forsome i 1 i t In this thesis we provide the exact value of the multicolor Ramsey numberR Pn1 Pn2 Pnt Ck for certain values of ni and k where Pn and Cn denote a path and acycle on n vertices respectively In addition we determine the 2 color hypergraph Ramsey k k k knumber of a k uniform loose 3 cycle or 4 cycle R C3 C3 3k 2 and R C4 C4 4k 3 for 3 3 3k 3 For more than three colors we could prove only that R C3 C3 C3 8 Nevertheless the r color Ramsey number of triangles for hypergraphs are much smaller than for graphs for r 3 3 3 3 r 5 R C3 C3 C3 3r Key WordsMulticolor Ramsey Number Hypergraph Loose Cycle Loose Path Introduction Since the 1970 s Ramsey theory has grown into one of the most active areas of researchwithin combinatorics overlapping variously with graph theory number theory geometry andlogic The graph case of the Ramsey numbers is de ned as follows Let G1 G2 Gt begraphs The graph Ramsey number R G1 G2 Gt is the smallest positive integer n suchthat if the edges of a complete graph Kn are partitioned into t disjoint color classes giving tgraphs H1 H2 Ht then at least one Hi has a subgraph isomorphic to Gi The existenceof such a positive integer is guaranteed by Ramsey s classical result 16 For t 3 there isa few results about multicolor Ramsey number R G1 G2 Gt A survey including someresults on Ramsey number of graphs can be found in 15 In this thesis we only concerned with undirected simple nite graphs and we follow 1 1
استاد راهنما :
غلامرضا اميدي
استاد مشاور :
بهناز عمومي
استاد داور :
سعيد اكبري، ابراهيم قرباني، جواد باقريان
