پديد آورنده :
يزدان پناه، مسعود
عنوان :
كاربردهاي تجزيه گراف كامل يال - رنگ آميزي شده
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه، 74ص.: مصور
استاد راهنما :
رامين جوادي
تاريخ نمايه سازي :
1394/08/06
استاد داور :
غلامرضا اميدي، بهناز عمومي
تاريخ ورود اطلاعات :
1396/10/05
چكيده انگليسي :
Some Applications of decompositions of Edge Colored Complete Graphs Masoud Yazdan Panah m yazdan@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Ramin Javadi rjavadi@cc iut ac ir 2010 MSC 05B05 05B15 Keywords asymptotic existence theorem decomposition Abstract In this thesis we survey the seminal papers of R M Wilson about the asymptotic existence theo rems for the decompositions of edge colored complete graphs into prespeci ed edge colored subgraphs Generally in these theorems it is proved that the obvious necessary condition for the existence of adecomposition the conditions on divisibility of the number of edges and the vertex degrees areasymptotically su cient for larg values of n A large family of combinatorial problems can be for r mulated or discussed in this language of graph decomposition Let Kn be a complete digraph on nvertices with exactly one edge of color i joining any vertex x to any other vertex y for every color i ina set of r colors Also let G be a collection of simple edge colored graphs The existence of certain r combinatorial structures can be seen to be equivalent to the existence of a G decomposition of Knfor some G and r Sometimes the correspondence is natural and immediate e g whist tournaments Steiner pentagon systems other instances require a translation and may appear somewhat arti cial For example both the existence of certain group divisible designs and the existence of resolvabledesigns can be expressed as such decompositions Given a family G of edge r colored digraphs we r may ask for which values of n the complete digraph Kn admits a G decomposition Of course we r are assuming that the r colors used for Kn are the same r colors that appear on edges of members ofG We state the existence result rst in the special case when G consists of a single graph G There r are two obvious necessary condition for the decomposition of Kn into subgraphs isomorphic to G r First the number of edges of each color in G should divids the number of edges of each color in Kn r i e n n 1 Also the vertex degree of each color in Kn i e n 1 should be written as a non
استاد راهنما :
رامين جوادي
استاد داور :
غلامرضا اميدي، بهناز عمومي
