The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The vertex separation number of a graph equals its path-width
Information Processing Letters
The vertex separation and search number of a graph
Information and Computation
Chordal completions of planar graphs
Journal of Combinatorial Theory Series B
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
Basic graph theory: paths and circuits
Handbook of combinatorics (vol. 1)
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
Theoretical Computer Science - Selected papers in honor of Manuel Blum
On the powers of graphs with bounded asteroidal number
Discrete Mathematics
The Complexity of the Approximation of the Bandwidth Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximating bandwidth by mixing layouts of interval graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Discrete Applied Mathematics
Graph drawings with few slopes
Computational Geometry: Theory and Applications
Discrete Applied Mathematics
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The interval degree id(G) of a graph G is defined to be the smallest max-degree of any interval supergraphs of G. One of the reasons for our interest in this parameter is that the bandwidth of a graph is always between id(G)/2 and id(G). We prove also that for any graph G the interval degree of G is at least the pathwidth of G2. We show that if G is an AT-free claw-free graph, then the interval degree of G is equal to the clique number of G2 minus one. Finally, we show that there is a polynomial time algorithm for computing the interval degree of AT-free claw-free graphs.