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A coloring using at most k colors is called a (proper) k-coloring. The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G). Sometimes γ(G) is used, since χ(G) is also used to denote the Euler characteristic of a graph.
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 ...
DSatur is known to be exact for bipartite graphs, [1] as well as for cycle and wheel graphs. [2] In an empirical comparison by Lewis in 2021, DSatur produced significantly better vertex colourings than the greedy algorithm on random graphs with edge probability p = 0.5 {\displaystyle p=0.5} , while in turn producing significantly worse ...
Using a strong edge coloring (and using two time slots for each edge color, one for each direction) would solve the problem but might use more time slots than necessary. Instead, they seek a coloring of the directed graph formed by doubling each undirected edge of the network, with the property that each directed edge uv has a different color ...
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. One player tries to ...
A graph G is said to be perfectly orderable if there is a sequence of its vertices with the property that, for any induced subgraph of G, a greedy coloring algorithm that colors the vertices in the induced sequence ordering is guaranteed to produce an optimal coloring. For a chordal graph, a perfect elimination ordering is a perfect ordering ...
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.