On the diameter of geometric path graphs of points in convex position

Authors:
Jou-Ming Chang;Ro-Yu Wu
Affiliations:
Department of Information Management, National Taipei College of Business, Taipei, Taiwan, ROC;Department of Industrial Engineering Management, Lunghwa University of Science and Technology, Taoyuan, Taiwan, ROC
Venue:
Information Processing Letters
Year:
2009

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Abstract

For a set S of n points in convex position in the plane, let P(S) denote the set of all plane spanning paths of S. The geometric path graph of S, denoted by G"n, is the graph with P(S) as its vertex set and two vertices P,Q@?P(S) are adjacent if and only if P and Q can be transformed to each other by means of a single edge replacement. Recently, Akl et al. [S.G. Akl, K. Islam, H. Meijer, On planar path transformation, Inform. Process. Lett. 104 (2007) 59-64] showed that the diameter of G"n is at most 2n-5. In this note, we derive the exact diameter of G"n for n=3.