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The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

The pentakis icosidodecahedron is the dual of the chamfered dodecahedron. It contains 42 vertices, 120 edges, and 80 faces. The canonical version has two distinct edge ...

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

A maximal subgraph of an undirected graph such that any two edges in the subgraph lie on a common simple cycle.

The Soicher graphs are three distance-regular graphs on 5346, 486, and 315 vertices, respectively. The first two are also distance-transitive but the third is not. The second ...

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

A generalized octagon GO(n,k) is a generalized polygon of order 8. GO(1,2) is the (3,8)-cage graph, the incidence graph of the Cremona-Richmond configuration, the cubic ...

The small dodecahemidodecahedron is the uniform polyhedron with Maeder index 51 (Maeder 1997), Wenninger index 91 (Wenninger 1989), Coxeter index 65 (Coxeter et al. 1954), ...