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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.
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 ...
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
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.
k-degenerate graphs have also been called k-inductive graphs. degree 1. The degree of a vertex in a graph is its number of incident edges. [2] The degree of a graph G (or its maximum degree) is the maximum of the degrees of its vertices, often denoted Δ(G); the minimum degree of G is the minimum of its vertex degrees, often denoted δ(G).
In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but ...
The degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta function at k 0, with infinite height there but area equal to 1. [citation needed] The cumulative distribution function of the univariate degenerate distribution is:
The 3-colorings of a path graph, which has degeneracy one. The diameter of this space of colorings is four: it takes four steps to get from either of the top two colorings to the bottom one. In the mathematics of graph coloring, Cereceda’s conjecture is an unsolved problem on the distance between pairs of colorings of sparse graphs.