
Terrain Visibility Graphs: Persistence is Not Enough
In this paper, we consider the Visibility Graph Recognition and Reconstr...
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4copwin graphs have at least 19 vertices
We show that the cop number of any graph on 18 or fewer vertices is at m...
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On the maximum number of non attacking rooks on a highdimensional simplicial chessboard
The simplicial rook graph 𝒮ℛ(m,n) is the graph whose vertices are vector...
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Persistent Betti numbers of random Čech complexes
We study the persistent homology of random Čech complexes. Generalizing ...
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The SingleFace Ideal Orientation Problem in Planar Graphs
We consider the ideal orientation problem in planar graphs. In this prob...
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The smallest nontrivial snarks of oddness 4
The oddness of a cubic graph is the smallest number of odd circuits in a...
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Adversary Detection in Neural Networks via Persistent Homology
We outline a detection method for adversarial inputs to deep neural netw...
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Terrain Visibility Graphs and Cyclic Polytope Triangulations
We prove a bijection between the triangulations of the 3dimensional cyclic polytope C(n, 3) and persistent graphs with n2 vertices. We show that under this bijection, the StasheffTamari orders naturally translate to subgraph inclusion. Moreover, we describe a connection to the second higher Bruhat order B(n2, 2). We also give an algorithm to efficiently enumerate all persistent graphs on n2 vertices and thus all triangulations of C(n, 3).
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