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» Planar Graphs, via Well-Orderly Maps and Trees
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WG
2004
Springer
13 years 9 months ago
Planar Graphs, via Well-Orderly Maps and Trees
The family of well-orderly maps is a family of planar maps with the property that every connected planar graph has at least one plane embedding which is a well-orderly map. We show...
Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse,...
CVPR
2010
IEEE
14 years 26 days ago
Beyond Trees: MRF Inference via Outer-Planar Decomposition
Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. t...
Dhruv Batra, Andrew Gallagher, Devi Parikh, Tsuhan...
FCT
2009
Springer
13 years 11 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
ICALP
2003
Springer
13 years 9 months ago
Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs
The (k, r)-center problem asks whether an input graph G has ≤ k vertices (called centers) such that every vertex of G is within distance ≤ r from some center. In this paper we ...
Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Ha...
COMBINATORICS
2004
84views more  COMBINATORICS 2004»
13 years 4 months ago
Planar Maps as Labeled Mobiles
We extend Schaeffer's bijection between rooted quadrangulations and welllabeled trees to the general case of Eulerian planar maps with prescribed face valences to obtain a bi...
J. Bouttier, P. Di Francesco, E. Guitter