Acute Constraints in Straight-Line Drawings of Planar Graphs

Akane SETO  Aleksandar SHURBEVSKI  Hiroshi NAGAMOCHI  Peter EADES  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.9   pp.994-1001
Publication Date: 2019/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.994
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: Graph algorithms
graph drawing,  1-planarity,  right angle crossing,  forbidden graph configurations,  

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Recent research on graph drawing focuses on Right-Angle-Crossing (RAC) drawings of 1-plane graphs, where each edge is drawn as a straight line and two crossing edges only intersect at right angles. We give a transformation from a restricted case of the RAC drawing problem to a problem of finding a straight-line drawing of a maximal plane graph where some angles are required to be acute. For a restricted version of the latter problem, we show necessary and sufficient conditions for such a drawing to exist, and design an O(n2)-time algorithm that given an n-vertex plane graph produces a desired drawing of the graph or reports that none exists.