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Graph coloring enjoys many practical applications as well as theoretical challenges. Beside the classical types of problems, different limitations can also be set on the graph, or on the way a color is assigned, or even on the color itself. It has even reached popularity with the general public in the form of the popular number puzzle Sudoku ...
Pages in category "Graph coloring" The following 82 pages are in this category, out of 82 total. This list may not reflect recent changes. ...
Graph coloring [2] [3]: GT4 Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph.
1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. 4 Trees. Toggle Trees subsection. ... Graph coloring game; Graph two-coloring; Harmonious coloring;
A 3-edge-coloring of the Desargues graph. In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green.
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.
In graph theory, a distinguishing coloring or distinguishing labeling of a graph is an assignment of colors or labels to the vertices of the graph that destroys all of the nontrivial symmetries of the graph. The coloring does not need to be a proper coloring: adjacent vertices are allowed to be given the same color. For the colored graph, there ...
An oriented chromatic number of a graph G is the fewest colors needed in an oriented coloring; it is usually denoted by (). The same definition can be extended to undirected graphs, as well, by defining the oriented chromatic number of an undirected graph to be the largest oriented chromatic number of any of its orientations .