On the Minimum Diameter among Orientations of CompleteMultipartite Graphs

• Main Authors: Chien-Yeh Chen, 陳建燁
• Other Authors: 張鎮華
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/27807474496205981423

碩士 === 國立臺灣大學 === 數學研究所 === 94 === On investigating the one-way street problem, Robbins proved that a connected graph has a strong orientation if and only if it has no bridges. An interesting and practical problem is that, besides the existence of a strong orientation, what is the minimum diameter of such an orientation. More precisely, for a given graph G, denote D(G) the family of all strong orientations of G. The object parameter then is d(G) = min{d(D) : D 2 D(G)}. Denote K(p1, p2, . . . , pn) the complete n-partite graph having pi vertices in the ith partite set. While it is known that 2< = d(K(p1,p2, . . . , pn)) < = 3 for n > = 3, there are still many ~d(K(p1, p2, . . . , pn)) remain un-determined. In this thesis, we establish some new results. We determine d(G) of some complete 3-partite graphs. Also, we find a family of complete multipartite graphs G with d(G)=2, for n>3.