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An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle. A pseudotree is therefore a connected pseudoforest and a forest ...

The disk model is the standard Boolean-Poisson model in two-dimensional continuum percolation theory. In particular, the disk model is characterized by the existence of a ...

The value for zeta(2)=sum_(k=1)^infty1/(k^2) (1) can be found using a number of different techniques (Apostol 1983, Choe 1987, Giesy 1972, Holme 1970, Kimble 1987, Knopp and ...

A two-dimensional affine geometry constructed over a finite field. For a field F of size n, the affine plane consists of the set of points which are ordered pairs of elements ...

A polynomial sequence p_n(x) is called the basic polynomial sequence for a delta operator Q if 1. p_0(x)=1, 2. p_n(0)=0 for all n>0, 3. Qp_n(x)=np_(n-1)(x). If p_n(x) is a ...

Some computations allow shortcuts which can be used to speed them up. Consider the operation of raising a number to a positive integer power. It is possible, for example, to ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

An edge subdivision is the insertion of a new vertex v_j in the middle of an exiting edge e=v_iv_k accompanied by the joining of the original edge endpoints with the new ...

The Laplacian spectral radius of a finite graph is defined as the largest value of its Laplacian spectrum, i.e., the largest eigenvalue of the Laplacian matrix (Lin et al. ...