A Study on Local Harmonious Problems

• Main Authors: Lin-yuan Wang, 王凌淵
• Other Authors: Tsung-wu Lin
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/71717411930930766780

碩士 === 東吳大學 === 資訊管理學系 === 98 === 　　The harmonious chromatic number of graph G, denoted h(G), is the least number of colors which can be used to color V(G) such that adjacent vertices are colored differently and each color-pair occurs on the vertices of an edge at most once. In this paper, we generalize the above problem to be the local harmonious chromatic problem. The local harmonious chromatic problem restricts that the different color-pair requirement is only asked to be satisfied for every edge within distance d for any vertex. We show that the local harmonious chromatic problem with d = 1 for general graphs is NP-complete. Besides, we also solve the local harmonious chromatic problem on paths and cycles.