Marcin Wrochna

Reconfiguration in bounded bandwidth and tree-depth

We show that several reconfiguration problems known to be PSPACE-complete remain so even when limited to graphs of bounded bandwidth. The essential step is noticing the similarity to very limited string rewriting systems, whose ability to directly simulate Turing Machines is classically known. This resolves a question posed open in [Bonsma P., 2012]. On the other hand, we show that a large class of reconfiguration problems becomes tractable on graphs of bounded treedepth, and that this result is in some sense tight.

Reconfiguring Independent Sets in Claw-Free Graphs

We present a polynomial-time algorithm that, given two independent sets in a claw-free graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w (not in S) such that the result is again an independent set. We also consider the more restricted model where v and w have to be adjacent.

Reconfiguration over Tree Decompositions

A vertex-subset graph problem

Fully polynomial-time parameterized computations for graphs and matrices of low treewidth

Q

Homomorphism Reconfiguration via Homotopy.

defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem

Cutwidth: obstructions and algorithmic aspects

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Linear Kernels for Edge Deletion Problems to Immersion-Closed Graph Classes

asks whether it is possible to transform one feasible solution for

Square-free graphs are multiplicative

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The step Sidorenko property and non-norming edge-transitive graphs

into another in at most

On Directed Feedback Vertex Set Parameterized by Treewidth

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