پديد آورنده :
احمدپور خرمي، قاسم
عنوان :
نتايج حدي براي ابرگراف هاي برج
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي(نظريه گراف و تركيبات)
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
غلامرضا اميدي اردلي
استاد مشاور :
مريم شاه سياه
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
عدد توران , دور برج
استاد داور :
غفار رئيسي، رامين جوادي
تاريخ ورود اطلاعات :
1395/07/18
چكيده انگليسي :
Extremal results for Berge hypergraphs Ghasem ahmadpour khorrami g ahmadpour@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Gholam Reza Omidi Ardali romidi@cc iut ac ir 2016 MSC 11T71 11G20 14Q20 68Q25 Keywords Tur n number Berge cycle G Berge hypergraph AbstractStudy of Tur n numbers is a main sub eld of extremal combinatorics Tur n problems are questionsof the following sort Let F be a family of graphs How many edges can a graph have if the graphcontains no member of F as a subgraph The rst Tur n type result was proved by Mantel in 1907 n2Mantel showed that if a graph on n vertices has more than edges then it must contain a triangle 4This result did not generate much attention until after Tur n proved a much more general theorem Tur n s seminal paper can easily be credited for popularizing and indeed starting this eld of study this is why it bears his name In this paper Tur n found the largest graphs which do not contain aKk for any xed k these easily stated problems are often quite di cult to solve the theory is quitedeep and the methods needed to solve these problems can be varied and complex We will ask thisquestion in the context of hypergraphs Let G be a graph and H be a hypergraph both on the samevertex set Berge s approach to the question of such generalization problems is the following Suppose we wantto nd an appropriate generalization of a graph G to a hypergraph The information contained inthe graph G can be expressed in an adjacency matrix or even in an incidence matrix a graph isan incidence structure of points and lines where each line is incident with exactly two points Nowif M G is the incidence matrix of the graph G the Berge hypergraph generalization of G is anyhypergraph H with incidence matrix M H where M G i j 1 M H i j 1 In other words thesame incidences occur in H or possibly more as in G We say that the hypergraph H is a Berge G ifthere is a bijection f E G E H such that for e E G we have e f e In other words givena graph G we can construct a Berge G by replacing each edge of G with a hyperedge that contains
استاد راهنما :
غلامرضا اميدي اردلي
استاد مشاور :
مريم شاه سياه
استاد داور :
غفار رئيسي، رامين جوادي
