کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4646579 1413648 2017 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the number of 7-cycles in regular n-tournaments
ترجمه فارسی عنوان
درباره تعداد هفت دوره تورنمت N منظم
کلمات کلیدی
مسابقات؛ مسابقات انتقالی؛ مسابقات به صورت محلی انتقالی؛ مسابقات منظم؛ مسابقات مضاعف منظم؛ مسابقات مانده درجه دوم
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
چکیده انگلیسی

For a regular tournament TT of odd order nn, let cm(T)cm(T) be the number of cycles of length mm in TT. It is well known according to U. Colombo (1964) that c4(T)≤c4(RLTn), where RLTn is the unique regular locally transitive tournament of order nn. In turn, in 1968, A. Kotzig proved that c4(DRn)≤c4(T)c4(DRn)≤c4(T), where DRnDRn is a doubly-regular tournament of order nn. However, the spectral tools allow us to simply show that the converse inequality c5(RLTn)≤c5(T)≤c5(DRn) holds. Recently we have proved that c6(T)≤c6(DRn)c6(T)≤c6(DRn) and conjectured that c6(RLTn)≤c6(T). For these values of mm, the same results can be also formulated for the trace trm(T)trm(T) of the mmth power of the adjacency matrix of TT. (We consider this quantity here because it equals the number of closed walks of length mm in TT.) In the present paper, we determine c7(DRn)c7(DRn) and c7(RLTn). Comparing c7(DRn)c7(DRn) with c7(RLTn) yields the inequality c7(RLTn)

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 2, 6 February 2017, Pages 264–285
نویسندگان
,