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» Induced trees in triangle-free graphs
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DAM
2010
81views more  DAM 2010»
13 years 7 months ago
The k-in-a-tree problem for graphs of girth at least k
For all integers k 3, we give an O(n4 ) time algorithm for the problem whose instance is a graph G of girth at least k together with k vertices and whose question is "Does G...
W. Liu, Nicolas Trotignon
COMBINATORICS
2000
114views more  COMBINATORICS 2000»
13 years 7 months ago
Trees and Matchings
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on ...
Richard Kenyon, James Gary Propp, David Bruce Wils...
JGT
2006
70views more  JGT 2006»
13 years 7 months ago
Vertex partitions of chordal graphs
Abstract: A k-tree is a chordal graph with no (k + 2)-clique. An -treepartition of a graph G is a vertex partition of G into `bags,' such that contracting each bag to a single...
David R. Wood
WG
1998
Springer
13 years 11 months ago
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
Bruno Courcelle, Johann A. Makowsky, Udi Rotics
COMBINATORICS
2004
100views more  COMBINATORICS 2004»
13 years 7 months ago
Lattice Structures from Planar Graphs
The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the p...
Stefan Felsner