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DCG
2011
13 years 4 months ago
Small Grid Embeddings of 3-Polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by O(27.55n ) = O(18...
Ares Ribó Mor, Günter Rote, Andr&eacut...
MFCS
1998
Springer
14 years 2 months ago
Facial Circuits of Planar Graphs and Context-Free Languages
It is known that a language is context-free iff it is the set of borders of the trees of recognizable set, where the border of a (labelled) tree is the word consisting of its leaf ...
Bruno Courcelle, Denis Lapoire
COMBINATORICS
2002
88views more  COMBINATORICS 2002»
13 years 9 months ago
Graph Color Extensions: When Hadwiger's Conjecture and Embeddings Help
Suppose G is r-colorable and P V (G) is such that the components of G[P] are far apart. We show that any (r + s)-coloring of G[P] in which each component is s-colored extends to ...
Michael O. Albertson, Joan P. Hutchinson
DAM
2011
13 years 4 months ago
Untangling planar graphs from a specified vertex position - Hard cases
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an ...
Mihyun Kang, Oleg Pikhurko, Alexander Ravsky, Math...
CCCG
2009
13 years 11 months ago
On Directed Graphs with an Upward Straight-line
In this paper we study the problem of computing an upward straight-line embedding of a directed graph G into a point set S, i.e. a planar drawing of G such that each vertex is map...
Carla Binucci, Emilio Di Giacomo, Walter Didimo, A...