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» Subgraph Isomorphism in Planar Graphs and Related Problems
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ALGOSENSORS
2004
Springer
15 years 3 months ago
On a Conjecture Related to Geometric Routing
We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance ...
Christos H. Papadimitriou, David Ratajczak
ALGORITHMICA
2006
138views more  ALGORITHMICA 2006»
14 years 10 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...
ESA
2010
Springer
136views Algorithms» more  ESA 2010»
14 years 11 months ago
Fast Minor Testing in Planar Graphs
Minor containment is a fundamental problem in Algorithmic Graph Theory, as numerous graph algorithms use it as a subroutine. A model of a graph H in a graph G is a set of disjoint ...
Isolde Adler, Frederic Dorn, Fedor V. Fomin, Ignas...
SWAT
1994
Springer
86views Algorithms» more  SWAT 1994»
15 years 1 months ago
Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees
We present sequential and parallel algorithms for various embedding problems on bounded degree partial k-trees and k-connected partial k-trees these include subgraph isomorphism a...
Arvind Gupta, Naomi Nishimura
DM
2010
131views more  DM 2010»
14 years 10 months ago
Planar graphs without adjacent cycles of length at most seven are 3-colorable
We prove that every planar graph in which no i-cycle is adjacent to a j-cycle whenever 3 i j 7 is 3-colorable and pose some related problems on the 3-colorability of planar grap...
Oleg V. Borodin, Mickaël Montassier, Andr&eac...