A Four-Color Algorithm in Triangulated Planar Graphs

• Main Author: 鄭國城
• Other Authors: 王有禮
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/15219086297922524604

碩士 === 國立臺灣科技大學 === 資訊工程系 === 90 === In general, a triangulated planar graph is four-colorable. In this thesis, we prove that it all internal vertices are of even degrees, then the triangulated planar graph is three-colorable. Moreover, a triangulated planar graph needs four colors when it contains an odd internal vertex. Either the odd internal vertex or one its neighbors needs to draw the fourth color. In this thesis, we propose an algorithm for solving the four color problem of triangulated planar graphs. The first step of our algorithm is to determine which vertices will be draw the fourth color. Then, we use the remaining three colors to draw the other vertices. The time complexity of our algorithm is O(m+n), where n is the order and m is the size of the graph.