Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings
SIAM Journal on Discrete Mathematics
Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer
SIAM Journal on Discrete Mathematics
Canonical Ordering Trees and Their Applications in Graph Drawing
Discrete & Computational Geometry
Improved visibility representation of plane graphs
Computational Geometry: Theory and Applications
Nearly Optimal Visibility Representations of Plane Graphs
SIAM Journal on Discrete Mathematics
Width-optimal visibility representations of plane graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
An application of well-orderly trees in graph drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Nearly optimal visibility representations of plane graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
New theoretical bounds of visibility representation of plane graphs
GD'04 Proceedings of the 12th international conference on Graph Drawing
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A visibility representation of a graph G is to represent the nodes of G with non-overlapping horizontal line segments such that the line segments representing any two distinct adjacent nodes are vertically visible to each other. If G is a plane graph, i.e., a planar graph equipped with a planar embedding, a visibility representation of G has the additional requirement of reflecting the given planar embedding of G. For the case that G is an n-node four-connected plane graph, we give an O(n)-time algorithm to produce a visibility representation of G with height at most @?n2@?+2@?n-22@?. To ensure that the first-order term of the upper bound is optimal, we also show an n-node four-connected plane graph G, for infinite number of n, whose visibility representations require heights at least n2.