The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Monotonicity in graph searching
Journal of Algorithms
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On the monotonicity of games generated by symmetric submodular functions
Discrete Applied Mathematics - Submodularity
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Computability of Width of Submodular Partition Functions
Combinatorial Algorithms
Partitions versus sets: A case of duality
European Journal of Combinatorics
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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The notion of submodular partition functions generalizes many of well-known tree decompositions of graphs. For fixed k, there are polynomial-time algorithms to determine whether a graph has tree-width, branch-width, etc. at most k. Contrary to these results, we show that there is no sub-exponential algorithm for determining whether the width of a given submodular partition function is at most two.