Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
On treewidth and minimum fill-in of asteroidal triple-free graphs
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
SIAM Journal on Discrete Mathematics
Domination and total domination on asteroidal triple-free graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Independent Sets in Asteroidal Triple-Free Graphs
SIAM Journal on Discrete Mathematics
A Lower Bound for Treewidth and Its Consequences
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Approximating the treewidth of AT-free graphs
Discrete Applied Mathematics
Treewidth computations II. Lower bounds
Information and Computation
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We define the stable degree s(G) of a graph G by s(G)= min U max v∈U dG(v), where the minimum is taken over all maximal independent sets U of G. For this new parameter we prove the following. Deciding whether a graph has stable degree at most k is NP-complete for every fixed k≥3; and the stable degree is hard to approximate. For asteroidal triple-free graphs and graphs of bounded asteroidal number the stable degree can be computed in polynomial time. For graphs in these classes the treewidth is bounded from below and above in terms of the stable degree.