TAILIEUCHUNG - Báo cáo toán học: "A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Point"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Points. | A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Points Weiwen Gu Department of Mathematics Michigan State University East Lansing USA guweiwen@ Submitted Jul 13 2010 Accepted Apr 12 2011 Published Apr 21 2011 Mathematics Subject Classification 05C88 Abstract In this paper we consider an oriented version of adjacency graphs of triangulations of bordered surfaces with marked points. We develop an algorithm that determines whether a given oriented graph is an oriented adjacency graph of a triangulation. If a given oriented graph corresponds to many triangulations our algorithm finds all of them. As a corollary we find out that there are only finitely many oriented connected graphs with non-unique associated triangulations. We also discuss a new algorithm which determines whether a given quiver is of finite mutation type. This algorithm is linear in the number of nodes and is more effective than the previously known one see 1 . Contents 1 Introduction 2 2 Definitions 5 3 Simplification 8 Nodes of Degree Eight. 8 Nodes of Degree Seven. 9 Nodes of Degree Six . 10 Nodes of Degree Five. 12 THE ELECTRONIC JOURNAL OF COMBINATORICS 18 2011 P91 1 4 Nodes of Degree Four 12 Four outward edges or four inward edges. 13 Three outward edges and one inward edge or three inward edges and one outward edge . 13 Two outward edges and two inward edges. 16 n 0. 16 n 1. 16 n 2. 17 n 3. 19 n 4. 20 5 Distinguishing the Neighborhoods when n 4 25 Node 1 is Connected to Nodes 2 and 3. 25 Node 1 is Connected to Node 2 but Disconnected from Node 3. 30 Node 1 is Disconnected from Nodes 2 3. 33 6 Simplification on Nodes of Degree Three 34 All edges have the same direction. 34 Two outward edges and one inward edge. 35 Determine the Decomposition. 41 References 45 1 Introduction In this paper we consider the properties of triangulations of surfaces

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