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A graph G having chromatic number chi(G)<=k is called a k-colorable graph (Harary 1994, p. 127). In contrast, a graph having chi(G)=k is said to be a k-chromatic graph. Note ...

The equations are x = 2/(sqrt(pi(4+pi)))(lambda-lambda_0)(1+costheta) (1) y = 2sqrt(pi/(4+pi))sintheta, (2) where theta is the solution to ...

The equations are x = ((lambda-lambda_0)(1+costheta))/(sqrt(2+pi)) (1) y = (2theta)/(sqrt(2+pi)), (2) where theta is the solution to theta+sintheta=(1+1/2pi)sinphi. (3) This ...

The Lambert cylindrical equal-area projection is a cylindrical equal-area projection with standard parallel phi_s=0 degrees.

The north pole is the point on a sphere with maximum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

The sinusoidal projection is an equal-area projection given by the transformation x = (lambda-lambda_0)cosphi (1) y = phi. (2) The inverse formulas are phi = y (3) lambda = ...

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

A conic projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cone with apex A which tangent to the ...

A set in R^n which can be reduced to one of its points, say P, by a continuous deformation, is said to be contractible. The transformation is such that each point of the set ...

A parametric latitude which gives a sphere equal surface area relative to an ellipsoid. The authalic latitude is defined by beta=sin^(-1)(q/(q_p)), (1) where ...