پديد آورنده :
باقري قوام آبادي، بهروز
عنوان :
پيرامون دو پوشش دوري گراف ها
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه،89ص.: مصور
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
بهناز عمومي
استاد مشاور :
عبادا... محموديان
تاريخ نمايه سازي :
29/2/93
استاد داور :
امير دانشگر، غلامرضا اميدي، رامين جوادي
كد ايرانداك :
ID629 دكتري
چكيده انگليسي :
Around the cycle double cover of graphs Behrooz Bagheri Gh b bagheri@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Behnaz Omoomi bomoomi@cc iut ac ir Advisor Dr E S Mahmoodian emahmood@sharif edu 2010 MSC 05C20 05C21 05C38 05C70 Keywords Cycle double cover Oriented perfect path double cover Small oreinted cycle doublecover Simultaneous edge coloring Circuit double cover AbstractA cycle double cover CDC C of a graph G is a collection of cycles in G such that every edge of Gbelongs to exactly two cycles of C In 1979 Seymour conjectured that every bridgeless graph has aCDC CDC conjecture This conjecture has a close relation to some famous concepts in graph theorysuch as nowhere zero 4 ow problem In 1988 the oriented version of this conjecture was stated Every bridgeless graph has a CDC in which every cycle can be oriented in such a way that every edgeof the graph is covered by two directed cycles in two di erent directions OCDC conjecture Anotherstronger conjecture about the cycle double cover problem is every bridgeless graph of order n has aCDC with at most n 1 cycles SCDC conjecture In this dissertation along with six chapters someproblems around the cycle double cover of graphs are studied An oriented perfect path double cover OPPDC of a graph G is a collection of directed pathsin the symmetric orientation Gs such that each edge of Gs lies in exactly one of the paths andeach vertex of G appears just once as a beginning and just once as end of a path In 8 Maxov and Ne et il conjectured that every graph except two complete graphs K3 and K5 has an OPPDC OPPDC conjecture and they claimed that the minimum degree of the minimal counterexample tothis conjecture is at least four In the proof of their claim when a graph is smaller than the minimalcounterexample they missed to consider the special cases K3 and K5 In Chapter 2 among someother results we presented a complete proof for this fact Theorem 1 2 If G is the minimal counterexample to the OPPDC conjecture then G 4
استاد راهنما :
بهناز عمومي
استاد مشاور :
عبادا... محموديان
استاد داور :
امير دانشگر، غلامرضا اميدي، رامين جوادي
