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The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

There are (at least) two graphs associated with Ellingham and Horton. These graphs on 54 and 78 nodes respectively, illustrated above, are examples of 3-connected bicubic ...

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

The de Grey-Haugstrup graphs are two 6-chromatic graphs on 47 and 48 vertices that are unit-distance in 3 dimensions (de Grey and Haugstrup 2020).

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by f(n) = (n+1; 3)+n+1 (1) = 1/6(n+1)(n^2-n+6) (2) = 1/6(n^3+5n+6), (3) where (a; ...

The Voronov-Neopryatnaya-Dergachev graphs are two graphs on 372 and 972 vertices which have unit-distance embeddings with all vertices on a sphere and chromatic number 5. The ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...