A vertex-face assignment for plane graphs

Authors:
Diane L. Souvaine;Csaba D. Tóth
Affiliations:
Department of Computer Science, Tufts University, Medford, MA, USA;Department of Mathematics, University of Calgary, AB, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2009

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Abstract

For every planar straight line graph (Pslg), there is a vertex-face assignment such that every vertex is assigned to at most two incident faces, and every face is assigned to all its reflex corners and one more incident vertex. Such an assignment allows us to augment every disconnected Pslg into a connected Pslg such that the degree of every vertex increases by at most two.