Convex drawings of graphs with non-convex boundary

Authors:
Seok-Hee Hong;Hiroshi Nagamochi
Affiliations:
School of Information Technologies, University of Sydney and NICTA;Department of Applied Mathematics and Physics, Kyoto University
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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Abstract

In this paper, we study a new problem of finding a convex drawing of graphs with a non-convex boundary. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. Such a drawing, called an inner-convex drawing, can be obtained in linear time.