Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Journal of Combinatorial Theory Series B
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
Graph-Theoretic Concepts in Computer Science
Recognizing digraphs of Kelly-width 2
Discrete Applied Mathematics
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The dag-width of directed graphs
Journal of Combinatorial Theory Series B
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Hunter and Kreutzer recently introduced the digraph width measure Kelly-width. The measure is based on a vertex elimination process that aims at bounding the out-degree of a vertex during the elimination. We refine the Kelly-width measure by bounding both the out-degree and the in-degree of a vertex. We show that the elimination process and a subgraph characterisation of Kelly-width naturally generalise to the refined notion. The main result of the paper is a game characterisation of the refined measure, which is a surprisingly non-trivial generalisation of the game for Kelly-width.