Simulation of large networks on smaller networks
Information and Control
The complexity of finding uniform emulations on fixed graphs
Information Processing Letters
The complexity of finding uniform emulations on paths and ring networks
Information and Computation
Tree-partitions of infinite graphs
Discrete Mathematics - Special volume: Designs and Graphs
Journal of Graph Theory
Some results on tree decomposition of graphs
Journal of Graph Theory
Discrete Mathematics
Journal of Algorithms
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Fractional colouring and Hadwiger's conjecture
Journal of Combinatorial Theory Series B
Tree-partite graphs and the complexity of algorithms
FCT '85 Fundamentals of Computation Theory
Partitioning into graphs with only small components
Journal of Combinatorial Theory Series B
Layout of Graphs with Bounded Tree-Width
SIAM Journal on Computing
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Computing straight-line 3D grid drawings of graphs in linear volume
Computational Geometry: Theory and Applications
Graph drawings with few slopes
Computational Geometry: Theory and Applications
IEEE Transactions on Computers
Vertex partitions of chordal graphs
Journal of Graph Theory
An efficient partitioning oracle for bounded-treewidth graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the model-checking of monadic second-order formulas with edge set quantifications
Discrete Applied Mathematics
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A tree-partition of a graph G is a proper partition of its vertex set into 'bags', such that identifying the vertices in each bag produces a forest. The width of a tree-partition is the maximum number of vertices in a bag. The tree-partition-width of G is the minimum width of a tree-partition of G. An anonymous referee of the paper [Guoli Ding, Bogdan Oporowski, Some results on tree decomposition of graphs, J. Graph Theory 20 (4) (1995) 481-499] proved that every graph with tree-width k=3 and maximum degree @D=1 has tree-partition-width at most 24k@D. We prove that this bound is within a constant factor of optimal. In particular, for all k=3 and for all sufficiently large @D, we construct a graph with tree-width k, maximum degree @D, and tree-partition-width at least (18-@e)k@D. Moreover, we slightly improve the upper bound to 52(k+1)(72@D-1) without the restriction that k=3.