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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 ...
Graph coloring has been studied as an algorithmic problem since the early 1970s: the chromatic number problem (see section § Vertex coloring below) is one of Karp's 21 NP-complete problems from 1972, and at approximately the same time various exponential-time algorithms were developed based on backtracking and on the deletion-contraction ...
To solve the problem of finding a subgraph = (,) in a given graph G = (V, E), where H can be a path, a cycle, or any bounded treewidth graph where | | = ( | |), the method of color-coding begins by randomly coloring each vertex of G with = | | colors, and then tries to find a colorful copy of H in colored G. Here, a graph is colorful if ...
This problem is a special case of a more general class of graph routing problems, known as call scheduling. In both the above problems, the goal is usually to minimise the number of colors used in the coloring. In different variants of path coloring, may be a simple graph, digraph or multigraph.
For this class of problems, the instance data P would be the integers m and n, and the predicate F. In a typical backtracking solution to this problem, one could define a partial candidate as a list of integers c = (c[1], c[2], …, c[k]), for any k between 0 and n, that are to be assigned to the first k variables x[1], x[2], …, x[k]. The ...
The road coloring problem is the problem of edge-coloring a directed graph with uniform out-degrees, in such a way that the resulting automaton has a synchronizing word. Trahtman (2009) solved the road coloring problem by proving that such a coloring can be found whenever the given graph is strongly connected and aperiodic.
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.
The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.