The Four Color Algorithm
2013, 18(5), pp.113-120
Publisher : The Korean Society Of Computer And Information
Research Area : Computer Science
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This paper proposes an algorithm that proves an NP-complete 4-color theorem by employing a linear time complexity where . The proposed algorithm accurately halves the vertex set of the graph into the Maximum Independent Set (MIS) and the Minimum Vertex Cover Set . It then assigns the first color to and the second to , which, along with , is halved from the connected graph , a reduced set of the remaining vertices. Subsequently, the third color is assigned to , which, along with, is halved from the connected graph , a further reduced set of the remaining vertices. Lastly, denotingas , the algorithm assigns the forth color to . The algorithm has successfully obtained the chromatic number with 100% probability, when applied to two actual map and two planar graphs. The proposed "four color algorithm", therefore, could be employed as a general algorithm to determine four-color for planar graphs.
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