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Monotone drawings of planar graphs
Author(s) -
Pach János,
Tóth Géza
Publication year - 2004
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.10168
Subject(s) - combinatorics , monotone polygon , planar graph , mathematics , graph , plane (geometry) , planar , crossing number (knot theory) , line (geometry) , line segment , discrete mathematics , geometry , computer science , computer graphics (images) , intersection (aeronautics) , engineering , aerospace engineering
Let G be a graph drawn in the plane so that its edges are represented by x ‐monotone curves, any pair of which cross an even number of times. We show that G can be redrawn in such a way that the x ‐coordinates of the vertices remain unchanged and the edges become non‐crossing straight‐line segments. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 39–47, 2004