Convex drawings of graphs with non-convex boundary constraints

Authors:
Seok-Hee Hong;Hiroshi Nagamochi
Affiliations:
School of Information Technologies, University of Sydney, Australia;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 6
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Abstract

In this paper, we study a new problem of convex drawing of planar graphs with non-convex boundary constraints, and call a drawing in which every inner-facial cycle is drawn as a convex polygon an inner-convex drawing. It is proved that every triconnected plane graph with the boundary fixed with a star-shaped polygon whose kernel has a positive area admits an inner-convex drawing. We also prove that every four-connected plane graph whose boundary is fixed with a crown-shaped polygon admits an inner-convex drawing. We present linear time algorithms to construct inner-convex drawings for both cases.