Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
The vertex separation and search number of a graph
Information and Computation
Obstruction set isolation for the gate matrix layout problem
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Triangulating multitolerance graphs
Discrete Applied Mathematics
All structured programs have small tree width and good register allocation
Information and Computation
Linear-time register allocation for a fixed number of registers
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Tree Decompositions of Small Diameter
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
The Treewidth of Java Programs
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
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Motivated by the desire to speed up dynamic programming algorithms for graphs of bounded treewidth, we initiate a study of the tradeoff between width and pathwidth of tree-decompositions. We therefore investigate the catwidth parameter cat w (G) which is the minimum width of any tree-decomposition (T, X) of a graph G when the pathwidth pw(T) of the tree T is 1. The catwidth parameter lies between the treewidth and the pathwidth of the graph, tw(G) ≤ catw(G) ≤ pw(G), and just as treewidth relates to chordal graphs and pathwidth relates to interval graphs, catwidth relates to what we call catval graphs. We introduce the notion of an extended asteroidal triple (XAT) and characterize catval graphs as the XAT-free chordal graphs. We provide alternative characterizations of these graphs, show that there are graph classes for which the various parameters differ by an arbitrary amount, and consider algorithms for computing catwidth.