
Monadic secondorder logic and the domino problem on selfsimilar graphs
We consider the domino problem on Schreier graphs of selfsimilar groups...
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Automorphism groups and Ramsey properties of sparse graphs
We study automorphism groups of sparse graphs from the viewpoint of topo...
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XRamanujan Graphs
Let X be an infinite graph of bounded degree; e.g., the Cayley graph of ...
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A local characterization for perfect plane neartriangulations
We derive a local criterion for a plane neartriangulated graph to be pe...
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Realization of shift graphs as disjointness graphs of 1intersecting curves in the plane
It is shown that shift graphs can be realized as disjointness graphs of ...
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Towards a short proof of the Fulek–Kynčl criterion for modulo 2 embeddability of graphs to surfaces
A connected graph K has a modulo 2 embedding to the sphere with g handle...
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A Topological Application of Labelled Natural Deduction
We use a labelled deduction system based on the concept of computational...
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Simulations and the Lamplighter group
We introduce a notion of "simulation" for labelled graphs, in which edges of the simulated graph are realized by regular expressions in the simulating graph, and prove that the tiling problem (aka "domino problem") for the simulating graph is at least as difficult as that for the simulated graph. We apply this to the Cayley graph of the "lamplighter group" L=ℤ/2≀ℤ, and more generally to "DiestelLeader graphs". We prove that these graphs simulate the plane, and thus deduce that the seeded tiling problem is unsolvable on the group L. We note that L does not contain any plane in its Cayley graph, so our undecidability criterion by simulation covers cases not covered by Jeandel's criterion based on translationlike action of a product of finitely generated infinite groups. Our approach to tiling problems is strongly based on categorical constructions in graph theory.
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