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Register a new userAn Algorithm for Continuously Edge Coloring a Set of Graphs
خوارزمية تلوين ضلعي مستمر لصف من البيانات
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محمد فراس الحلبي( باحث )
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كما هو معروف فإن مسألة تلوين بيان باستخدام أقل عدد من الألوان هي مسألة معقدة (NP-Hard) المشكلة تتلخص في كيفية تلوين عقد بيان بأقل عدد ممكن من الألوان . و بحيث لا يكون لأي عقدتين متجاورتين اللون نفسه، أو كيف يمكن تلوين أضلاع هذا البيان بأقل عدد ممكن من الألون بحيث لا يكون لضلعين يشتركان بعقدة اللون نفسه. نقدم في هذه الورقة البحثية خوارزمية تلوين جديدة لأضلاع بيان. هذه الخوارزمية تُمكننا من الحصول على تلوين ضلعي مستمر لصف من البيانات الشهيرة.
As it’s known, The Graph k-Colorability Problem (GCP) is a wellknown NP-Hard Problem. This problem consists in finding the k minimum number of colors to paint the vertices of a graph in such a way that any two adjoined vertices, which are connected by an edge, have always different colors. In another words how can we color the edges of a graph in such a way that any two edges joined by a vertex have always different colors? In this paper we introduce a new effective algorithm for coloring the edges of the graph. Our proposed algorithm enables us to achieve a Continuously Edge Coloring (CEC) for a set of known graphs.
References used
BARENBOIM, L.; ELKIN, M., 2009 - Distributed (Δ+1)-coloring in linear (in Δ) time, Proceedings of the 41st Symposium on Theory of Computing, pp. 111–120, ISBN 978-1-60558-506-2
BEIGEL, R., 2005 - 3-coloring in time O(1.3289n), Journal of Algorithms, 54 (2): 168–204
BRÉLAZ, D., 1979 - New Methods to Color the Vertices of a Graph, Communications of the ACM, 22 (4): 251–256
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