scholarly journals Canonical trees of tree-decompositions

2022 ◽  
Vol 152 ◽  
pp. 1-26
Author(s):  
Johannes Carmesin ◽  
Matthias Hamann ◽  
Babak Miraftab
Keyword(s):  
Tree Decompositions

AN IMPROVED ALGORITHM FOR FINDING TREE DECOMPOSITIONS OF SMALL WIDTH

2000 ◽  
Vol 11 (03) ◽  
pp. 365-371 ◽  
Author(s):  
LJUBOMIR PERKOVIĆ ◽  
BRUCE REED
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Tree Decomposition ◽  
Linear Time Algorithm ◽  
Input Graph ◽  
Primary Motivation ◽  
Small Width ◽  
Tree Decompositions ◽  
Improved Algorithm

We present a modification of Bodlaender's linear time algorithm that, for constant k, determine whether an input graph G has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k then a subgraph G′ of G of treewidth greater than k is returned along with a tree decomposition of G′ of width at most 2k. A consequence is that the fundamental disjoint rooted paths problem can now be solved in O(n2) time. This is the primary motivation of this paper.

scholarly journals Tree decompositions with small cost

2005 ◽  
Vol 145 (2) ◽  
pp. 143-154 ◽  
Author(s):  
Hans L. Bodlaender ◽  
Fedor V. Fomin
Keyword(s):  
Tree Decompositions

scholarly journals Two Short Proofs Concerning Tree-Decompositions

2002 ◽  
Vol 11 (6) ◽  
pp. 541-547 ◽  
Author(s):  
PATRICK BELLENBAUM ◽  
REINHARD DIESTEL
Keyword(s):  
Duality Theorem ◽  
Finite Graph ◽  
Tree Decomposition ◽  
Tree Width ◽  
Tree Decompositions

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.

Finding good tree decompositions by local search

2009 ◽  
Vol 32 ◽  
pp. 43-50 ◽  
Author(s):  
Stan van Hoesel ◽  
Bert Marchal
Keyword(s):  
Local Search ◽  
Tree Decompositions

Improving dynamic programming on tree decompositions

2015 ◽  
pp. 357-375
Author(s):  
Marek Cygan ◽  
Fedor V. Fomin ◽  
Łukasz Kowalik ◽  
Daniel Lokshtanov ◽  
Dániel Marx ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Tree Decompositions

scholarly journals Minimum size tree-decompositions

2018 ◽  
Vol 245 ◽  
pp. 109-127 ◽  
Author(s):  
Bi Li ◽  
Fatima Zahra Moataz ◽  
Nicolas Nisse ◽  
Karol Suchan
Keyword(s):  
Minimum Size ◽  
Tree Decompositions

scholarly journals Pebble Game Algorithms and (k,l)-Sparse Graphs

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Audrey Lee ◽  
Ileana Streinu
Keyword(s):  
Efficient Algorithms ◽  
Sparse Graphs ◽  
Edge Disjoint ◽  
International Audience ◽  
Tree Decompositions ◽  
Pebble Game

International audience A multi-graph $G$ on n vertices is $(k,l)$-sparse if every subset of $n'≤n$ vertices spans at most $kn'-l$ edges, $0 ≤l < 2k$. $G$ is tight if, in addition, it has exactly $kn - l$ edges. We characterize $(k,l)$-sparse graphs via a family of simple, elegant and efficient algorithms called the $(k,l)$-pebble games. As applications, we use the pebble games for computing components (maximal tight subgraphs) in sparse graphs, to obtain inductive (Henneberg) constructions, and, when $l=k$, edge-disjoint tree decompositions.

scholarly journals Multicut Algorithms via Tree Decompositions

2010 ◽  
pp. 167-179 ◽  
Author(s):  
Reinhard Pichler ◽  
Stefan Rümmele ◽  
Stefan Woltran
Keyword(s):  
Tree Decompositions
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