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ALGORITHMICA
2006
138views more  ALGORITHMICA 2006»
13 years 3 months ago
Planar Graph Coloring Avoiding Monochromatic Subgraphs: Trees and Paths Make It Difficult
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detail...
Hajo Broersma, Fedor V. Fomin, Jan Kratochví...
DAM
2008
93views more  DAM 2008»
13 years 3 months ago
Planar graph bipartization in linear time
For each constant k, we present a linear time algorithm that, given a planar graph G, either finds a minimum odd cycle vertex transversal in G or guarantees that there is no transv...
Samuel Fiorini, Nadia Hardy, Bruce A. Reed, Adrian...
DM
2010
91views more  DM 2010»
13 years 3 months ago
Adjacency posets of planar graphs
In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimensio...
Stefan Felsner, Ching Man Li, William T. Trotter
DCG
2010
135views more  DCG 2010»
13 years 3 months ago
Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices
This paper shows that any planar graph with n vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this...
Hazel Everett, Sylvain Lazard, Giuseppe Liotta, St...
CORR
2008
Springer
96views Education» more  CORR 2008»
13 years 3 months ago
Tree-width of hypergraphs and surface duality
In Graph Minors III, Robertson and Seymour write:"It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal -- indeed, w...
Frédéric Mazoit
CORR
2010
Springer
105views Education» more  CORR 2010»
13 years 3 months ago
Exact Shortest Path Queries for Planar Graphs Using Linear Space
We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar gr...
Shay Mozes, Christian Sommer
CORR
2008
Springer
98views Education» more  CORR 2008»
13 years 3 months ago
Void Traversal for Guaranteed Delivery in Geometric Routing
Geometric routing algorithms like GFG (GPSR) are lightweight, scalable algorithms that can be used to route in resource-constrained ad hoc wireless networks. However, such algorith...
Mikhail Nesterenko, Adnan Vora
COR
2008
95views more  COR 2008»
13 years 3 months ago
Good triangulations yield good tours
Consider the following heuristic for planar Euclidean instances of the Traveling Salesman Problem (TSP): select a subset of the edges which induces a planar graph, and solve eithe...
Adam N. Letchford, Nicholas A. Pearson
APPML
2007
101views more  APPML 2007»
13 years 3 months ago
Extension of a theorem of Whitney
It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triang...
Paul C. Kainen, Shannon Overbay
SODA
2000
ACM
121views Algorithms» more  SODA 2000»
13 years 5 months ago
Coloring powers of planar graphs
We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
Geir Agnarsson, Magnús M. Halldórsso...