14527

1366 دكتري

دكتري

رياضي

اصفهان : دانشگاه صنعتي اصفهان

1397

[دوازده]، [84]ص. : مصور،‌ جدول،‌ نمودار

غلامرضا اميدي

غفار رييسي

فارسي به انگليسي; انگليسي به فارسي

امير دانشگر،‌ عليرضا عبداللهي، بهناز عمومي

1398/01/27

كتابنامه

رياضي

رياضي

1398/02/02

ID1366 دكتري

A classification of nonabelian simple 3 BCI groups Zahra Rahimi zahra rahimi@math iut ac ir January 9 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Gholamreza OmidiAdvisor Dr Ghafar RaeisiMSC 2010 05C65 05C55 05D10Keywords Ramsey numbers stripes monochromatic cycle Szemer di s regularity lemma Abstract This M Sc thesis is based on the following papers Z Schelp s problem for three odd cycles Submitted T R Z Stars versus stripes Ramsey numbers in multicoloring European J O G R R G R Combin 67 2018 266 274 For given graphs G1 G2 Gt the multicolor Ramsey number R G1 G2 Gt is the smallest positiveinteger n such that if the edges of the 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 In this thesis for positive integerst1 t2 ts and n1 n2 nc the multicolor Ramsey number R St1 St2 Sts n1 K2 n2 K2 nc K2 is computed where nK2 denotes a matching stripe of size n i e n pairwise disjoint edges and Sn is a star with nedges This result generalizes and strengthens significantly a well known result of Cockayne and Lorimer and also aknown result of Gy rf s and S rk zy Kohayakava et al proved that for sufficiently large odd n R Cn Cn Cn 4n 3 i e when n is odd and largeenough every 3 coloring of the edges of the complete graph on 4n 3 vertices K4n 3 contains a monochromaticCn Hear we prove a Ramsey type problem with the similar result Consider a graph G on N 4n 3 vertices where n is sufficiently large odd integer and let G 7N 8 We show asymptotically that every 3 coloring ofthe edges of G contains a monochromatic Cn More pricisely we show that for every 0 there exists n0 suchthat for every odd n n0 and every graph G on 4 n vertices with G 7 2 n each colouring ofthe edges of G with three colours leads to a monochromatic cycle of length n For the proof we show that in every3 coloring of the edges of G there exists a color which contains a matching saturating at least n vertices containedin a component in this color which is non bipartite Then using Szemer di s regularity lemma we will show howexistance of Cn follows from existance of this matching

غلامرضا اميدي

غفار رييسي

امير دانشگر،‌ عليرضا عبداللهي، بهناز عمومي