کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777035 | 1413649 | 2017 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On acyclic edge-coloring of complete bipartite graphs
ترجمه فارسی عنوان
بر روی لبه های آسیلیکال رنگ آمیزی گرافهای دو طرفه کامل
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کلمات کلیدی
لبه رنگ آسیلیکال، شاخص رنگی آسیکلیک، تطبیق کامل، کامل 1-تقسیم بندی، نمودار دو طرفه کامل
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
An acyclic edge-coloring of a graph is a proper edge-coloring without bichromatic (2-colored) cycles. The acyclic chromatic index of a graph G, denoted by aâ²(G), is the least integer k such that G admits an acyclic edge-coloring using k colors. Let Î=Î(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by Kn,n. Basavaraju, Chandran and Kummini proved that aâ²(Kn,n)â¥n+2=Î+2 when n is odd. Basavaraju and Chandran provided an acyclic edge-coloring of Kp,p using p+2 colors and thus establishing aâ²(Kp,p)=p+2=Î+2 when p is an odd prime. The main tool in their approach is perfect 1-factorization of Kp,p. Recently, following their approach, Venkateswarlu and Sarkar have shown that K2pâ1,2pâ1 admits an acyclic edge-coloring using 2p+1 colors which implies that aâ²(K2pâ1,2pâ1)=2p+1=Î+2, where p is an odd prime. In this paper, we generalize this approach and present a general framework to possibly get an acyclic edge-coloring of Kn,n which possesses a perfect 1-factorization using n+2=Î+2 colors. In this general framework, using number theoretic techniques, we show that Kp2,p2 admits an acyclic edge-coloring with p2+2 colors and thus establishing aâ²(Kp2,p2)=p2+2=Î+2 when p is an odd prime.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 3, March 2017, Pages 481-493
Journal: Discrete Mathematics - Volume 340, Issue 3, March 2017, Pages 481-493
نویسندگان
Ayineedi Venkateswarlu, Santanu Sarkar, Sai Mali Ananthanarayanan,