Vertex coloring where every color pairing appears at least once
Complete coloring of the Clebsch graph with 8 colors. Every pair of colors appears on at least one edge. No complete coloring with more colors exists: in any 9-coloring some color would appear only at one vertex, and there would not be enough neighboring vertices to cover all pairs involving that color. Therefore, the achromatic number of the Clebsch graph is 8.
In graph theory, a complete coloring is a (proper) vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices. Equivalently, a complete coloring is minimal in the sense that it cannot be transformed into a proper coloring with fewer colors by merging pairs of color classes. The achromatic numberψ(G) of a graph G is the maximum number of colors possible in any complete coloring of G.
A complete coloring is the opposite of a harmonious coloring, which requires every pair of colors to appear on at most one pair of adjacent vertices.
In graph theory, a completecoloring is a (proper) vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices. Equivalently...
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...
at most one pair of adjacent vertices. It is the opposite of the completecoloring, which instead requires every color pairing to occur at least once...
edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem...
achromatic number of a graph is the maximum number of colors in a completecoloring. acyclic 1. A graph is acyclic if it has no cycles. An undirected...
path with three edges has a complete 3-coloring. Exact colorings are closely related to harmonious colorings (colorings in which each pair of colors...
the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring is a coloring of the vertices of a...
tries to successfully complete the coloring of the graph, when the other one tries to prevent him from achieving it. The vertex coloring game was introduced...
Food coloring, color additive or colorant is any dye, pigment, or substance that imparts color when it is added to food or beverages. Colorants can be...
trees. A complete bipartite graph Km,n has a maximum matching of size min{m,n}. A complete bipartite graph Kn,n has a proper n-edge-coloring corresponding...
In graph theory, a branch of mathematics, list coloring is a type of graph coloring where each vertex can be restricted to a list of allowed colors. It...
theory, total coloring is a type of graph coloring on the vertices and edges of a graph. When used without any qualification, a total coloring is always assumed...
In graph theory, an acyclic coloring is a (proper) vertex coloring in which every 2-chromatic subgraph is acyclic. The acyclic chromatic number A(G) of...
In graph theory, circular coloring is a kind of coloring that may be viewed as a refinement of the usual graph coloring. The circular chromatic number...
graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels...
be a coloring for the original graph. As Graph Coloring is an NP-Hard problem and Register Allocation is in NP, this proves the NP-completeness of the...
them outside the plane. Such construction makes the problem equivalent to coloring a map on a torus (a surface of genus 1), which requires up to 7 colors...
In graph theory, oriented graph coloring is a special type of graph coloring. Namely, it is an assignment of colors to vertices of an oriented graph that...
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No...
not all graphs allow interval edge coloring. A simple family of graphs that allows interval edge coloring is complete graph of even order and a counter...
Annatto (/əˈnætoʊ/ or /əˈnɑːtoʊ/) is an orange-red condiment and food coloring derived from the seeds of the achiote tree (Bixa orellana), native to tropical...
endpoints of differing colors, as is required in the graph coloring problem. In contrast, such a coloring is impossible in the case of a non-bipartite graph,...
In the mathematical field of graph theory, a star coloring of a graph G is a (proper) vertex coloring in which every path on four vertices uses at least...
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