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Theory of Computation

A connected bipartite graph is called Hamilton-laceable, a term apparently introduced in Simmons (1978), if it has a u-v Hamiltonian path for all pairs of vertices u and v, ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

The nth Beraha constant (or number) is given by B(n)=2+2cos((2pi)/n). B(5) is phi+1, where phi is the golden ratio, B(7) is the silver constant, and B(10)=phi+2. The ...

The bound for the number of colors which are sufficient for map coloring on a surface of genus g, gamma(g)=|_1/2(7+sqrt(48g+1))_| is the best possible, where |_x_| is the ...

Solving the nome q for the parameter m gives m(q) = (theta_2^4(q))/(theta_3^4(q)) (1) = (16eta^8(1/2tau)eta^(16)(2tau))/(eta^(24)(tau)), (2) where theta_i(q)=theta_i(0,q) is ...

Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

Miller's rules, originally devised to restrict the number of icosahedron stellations to avoid, for example, the occurrence of models that appear identical but have different ...