کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4656833 | 1632984 | 2014 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Tournaments with near-linear transitive subsets
ترجمه فارسی عنوان
مسابقات با زیر مجموعه های پیوندی نزدیک
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
Let H be a tournament, and let ϵâ¥0 be a real number. We call ϵ an “ErdÅs-Hajnal coefficient” for H if there exists c>0 such that in every tournament G not containing H as a subtournament, there is a transitive subset of cardinality at least c|V(G)|ϵ. The ErdÅs-Hajnal conjecture asserts, in one form, that every tournament H has a positive ErdÅs-Hajnal coefficient. This remains open, but recently the tournaments with ErdÅs-Hajnal coefficient 1 were completely characterized. In this paper we provide an analogous theorem for tournaments that have an ErdÅs-Hajnal coefficient larger than 5/6; we give a construction for them all, and we prove that for any such tournament H there are numbers c,d such that, if a tournament G with |V(G)|>1 does not contain H as a subtournament, then V(G) can be partitioned into at most c(logâ¡(|V(G)|))d transitive subsets.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 109, November 2014, Pages 228-249
Journal: Journal of Combinatorial Theory, Series B - Volume 109, November 2014, Pages 228-249
نویسندگان
Krzysztof Choromanski, Maria Chudnovsky, Paul Seymour,