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In graph theory, a path in an edge-colored graph is said to be rainbow if no color repeats on it. A graph is said to be rainbow-connected (or rainbow colored ) if there is a rainbow path between each pair of its vertices .
Given an edge-colored graph G = (V,E), a rainbow matching M in G is a set of pairwise non-adjacent edges, that is, no two edges share a common vertex, such that all the edges in the set have distinct colors. A maximum rainbow matching is a rainbow matching that contains the largest possible number of edges.
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring .
In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V 1, …, V m, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following ...
In graph theory, path coloring usually refers to one of two problems: The problem of coloring a (multi)set of paths R {\displaystyle R} in graph G {\displaystyle G} , in such a way that any two paths of R {\displaystyle R} which share an edge in G {\displaystyle G} receive different colors.
A graph coloring associates each vertex with a color drawn from a set of colors, in such a way that every edge has two different colors at its endpoints. A frequent goal in graph coloring is to minimize the total number of colors that are used; the chromatic number of a graph is this minimum number of colors. [1]
Quick-cooking chicken cutlets are coated in a garlic cream sauce, while spinach adds a boost of color and nutrition in this easy, one-skillet recipe. View Recipe. Chicken & Zucchini Casserole.
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.