Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Linear time algorithms for NP-hard problems restricted to partial k-trees
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Basic graph theory: paths and circuits
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A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
SIAM Journal on Computing
Topological minors in graphs of large girth
Journal of Combinatorial Theory Series B
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A High Girth Graph Construction
SIAM Journal on Discrete Mathematics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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On the maximum cardinality search lower bound for treewidth
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Isoperimetric Problem and Meta-fibonacci Sequences
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
On balanced CSPs with high treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Treewidth computations II. Lower bounds
Information and Computation
Computing the girth of a planar graph in linear time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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The length of the shortest cycle in a graph G is called the girth of G. In particular, we show that if G has girth at least g and average degree at least d, then tw(G) = Ω(1/g+1 (d - 1)⌊(g - 1)/2⌋). In view of a famous conjecture regarding the existence of graphs with girth g, minimum degree δ and having at most c(δ - 1)⌊(g - 1)/2⌋ vertices (for some constant c), this lower bound seems to be almost tight (but for a multiplicative factor of g + 1).