Characterization and recognition of partial 3-trees
SIAM Journal on Algebraic and Discrete Methods
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
A decomposition algorithm for network reliability evaluation
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Achievable sets, brambles, and sparse treewidth obstructions
Discrete Applied Mathematics
On the maximum cardinality search lower bound for treewidth
Discrete Applied Mathematics
Tree decomposition and discrete optimization problems: A survey
Cybernetics and Systems Analysis
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Treewidth computations I. Upper bounds
Information and Computation
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Treewidth computations II. Lower bounds
Information and Computation
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Treewidth lower bounds with brambles
ESA'05 Proceedings of the 13th annual European conference on Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Degree-Based treewidth lower bounds
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
New upper bound heuristics for treewidth
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
On the maximum cardinality search lower bound for treewidth
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Kernel bounds for structural parameterizations of pathwidth
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
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The notion of tree-decomposition has very strong theoretical interest related to NP-Hard problems. Indeed, several studies show that it can be used to solve many basic optimization problems in polynomial time when the treewidth is bounded. So, given an arbitrary graph, its decomposition and its treewidth have to be determined, but computing the treewidth of a graph is NP-Hard. Hence, several papers present heuristics with computational experiments, but for many instances of graphs, the heuristic results are far from the best lower bounds. The aim of this paper is to propose new lower and upper bounds for the treewidth. We tested them on the well known DIMACS benchmark for graph coloring, so we can compare our results to the best bounds of the literature. We improve the best lower bounds dramatically, and our heuristic method computes good bounds within a very small computing time.