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In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of k for which it is k-degenerate.
For continuous time, the Wiener–Khinchin theorem says that if is a wide-sense-stationary random process whose autocorrelation function (sometimes called autocovariance) defined in terms of statistical expected value = [() ()] <,,, where the asterisk denotes complex conjugate, then there exists a monotone function in the frequency domain < <, or equivalently a non negative Radon measure on ...
A graph is said to be k-generated if for every subgraph H of G, the minimum degree of H is at most k. Incidence chromatic number of k-degenerated graphs G is at most ∆(G) + 2k − 1. Incidence chromatic number of K 4 minor free graphs G is at most ∆(G) + 2 and it forms a tight bound. Incidence chromatic number of a planar graph G is at most ...
A degenerate conic is a conic section (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. A point is a degenerate circle, namely one with radius 0. [1] The line is a degenerate case of a parabola if the parabola resides on a tangent plane.
A stationary Gauss–Markov process with variance (()) = and time constant has the following properties.. Exponential autocorrelation: () = | |.; A power spectral density (PSD) function that has the same shape as the Cauchy distribution: () = +. (Note that the Cauchy distribution and this spectrum differ by scale factors.)
A single realization of a one-dimensional Wiener process A single realization of a three-dimensional Wiener process. In mathematics, the Wiener process (or Brownian motion, due to its historical connection with the physical process of the same name) is a real-valued continuous-time stochastic process discovered by Norbert Wiener.
The computation of the Hausdorff dimension of the graph of the classical Weierstrass function was an open problem until 2018, while it was generally believed that = + <. [6] [7] That D is strictly less than 2 follows from the conditions on and from above. Only after more than 30 years was this proved rigorously.
There is a notion of degree of outerplanarity. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is said to be k-outerplanar if removing the vertices on the outer face results in a (k − 1)-outerplanar embedding. A graph is k-outerplanar if it has a k-outerplanar embedding. [16]