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An edge switch is an operation which makes a local change in a graph whi...
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Symmetric binary Steinhaus triangles and parityregular Steinhaus graphs
A binary Steinhaus triangle is a triangle of zeroes and ones that points...
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DegreeSketch: Distributed Cardinality Sketches on Massive Graphs with Applications
We present DegreeSketch, a semistreaming distributed sketch data struct...
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Triangledegrees in graphs and tetrahedron coverings in 3graphs
We investigate a covering problem in 3uniform hypergraphs (3graphs): g...
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SingleStrip Triangulation of Manifolds with Arbitrary Topology
Triangle strips have been widely used for efficient rendering. It is NP...
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Any Regular Polyhedron Can Transform to Another by O(1) Refoldings
We show that several classes of polyhedra are joined by a sequence of O(...
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Multicast Triangular Semilattice Network
We investigate the structure of the code graph of a multicast network th...
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A triangle process on regular graphs
Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at least one triangle. Triangle switches can be used to define Markov chains which generate graphs with a given degree sequence and with many more triangles (3cycles) than is typical in a uniformly random graph with the same degrees. We show that the set of triangle switches connects the set of all dregular graphs on n vertices, for all d≥ 3. Hence, any Markov chain which assigns positive probability to all triangle switches is irreducible on these graphs. We also investigate this question for 2regular graphs.
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