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COMBINATORICS
2002
87views more  COMBINATORICS 2002»
14 years 9 months ago
Map Genus, Forbidden Maps, and Monadic Second-Order Logic
A map is a graph equipped with a circular order of edges around each vertex. These circular orders represent local planar embeddings. The genus of a map is the minimal genus of an...
Bruno Courcelle, V. Dussaux
MFCS
1998
Springer
15 years 1 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
CORR
2010
Springer
103views Education» more  CORR 2010»
14 years 9 months ago
On Graph Crossing Number and Edge Planarization
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
FCT
2009
Springer
15 years 4 months ago
Martingales on Trees and the Empire Chromatic Number of Random Trees
We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...
Colin Cooper, Andrew R. A. McGrae, Michele Zito
IJBC
2002
86views more  IJBC 2002»
14 years 9 months ago
Symbolic Dynamics from homoclinic tangles
We give a method for finding symbolic dynamics for a planar diffeomorphism with a homoclinic tangle. The method only requires a finite piece of tangle, which can be computed with ...
Pieter Collins