Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Combinatorica
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
An introduction to parallel algorithms
An introduction to parallel algorithms
Basic graph theory: paths and circuits
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Treewidth for graphs with small chordality
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
SIAM Journal on Computing
Coloring graphs with sparse neighborhoods
Journal of Combinatorial Theory Series B
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On the maximum cardinality search lower bound for treewidth
Discrete Applied Mathematics
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
On balanced CSPs with high treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Isoperimetric inequalities and the width parameters of graphs
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Treewidth computations II. Lower bounds
Information and Computation
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We give a lower bound for the treewidth of a graph in terms of the second smallest eigenvalue of its Laplacian matrix. We use this lower bound to show that the treewidth of a d-dimensional hypercube is at least ⌊3ċ2d/(2(d + 4))⌋ - 1. The currently known upper bound is O(2d/√d). We generalize this result to Hamming graphs. We also observe that every graph G on n vertices, with maximum degree Δ (1) contains an induced cycle (chordless cycle) of length at least 1 + logΔ (µn/8) (provided G is not acyclic), (2) has a clique minor Kh for some h = Ω((nµ2/(Δ + 2µ)2)1/3), where µ is the second smallest eigenvalue of the Laplacian matrix of G.