Motivated by the algorithmic study of 3-dimensional manifolds, we explore the structural relationship between the JSJ decomposition of a given 3-manifold and its triangulations. Building on work of Bachman, Derby-Talbot and Sedgwick, we show that a "sufficiently complicated" JSJ decomposition of a 3-manifold enforces a…
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5 results for “pathwidth”
Improved pathwidth bound for hyperbolic 3-manifolds.
problem Finding a more efficient triangulation for hyperbolic 3-manifolds.
method Synthesis of tools from 3-manifold theory: Heegaard splittings, amalgamations, and thick-thin decomposition.
result Volume provides a linear upper bound on pathwidth of triangulations.
In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic …
Graphs on surfaces have a 2-dimensional large scale structure.
problem Understanding the large scale structure of graphs on surfaces.
method Proving asymptotic dimension for specific graph classes and surfaces.
result Graphs on surfaces have an asymptotic dimension of 2.
Study on teaching complexity in graphs, proving hardness and tractability.
problem Computing the minimum number of examples per concept for teaching.
method Classical and parameterized complexity analysis, NP-hardness, upper and lower bounds, fixed-parameter tractability.
result Nearly complete understanding of teaching complexity in graphs.