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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.
Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring ...
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;
Col is a pencil and paper game, specifically a map-coloring game, involving the shading of areas in a line drawing according to the rules of graph coloring.With each move, the graph must remain proper (no two areas of the same colour may touch), and a player who cannot make a legal move loses.
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 ...
Pages in category "Graph coloring" The following 82 pages are in this category, out of 82 total. This list may not reflect recent changes. ...
Exact coloring of the complete graph K 6. Every n-vertex complete graph K n has an exact coloring with n colors, obtained by giving each vertex a distinct color. Every graph with an n-color exact coloring may be obtained as a detachment of a complete graph, a graph obtained from the complete graph by splitting each vertex into an independent set and reconnecting each edge incident to the ...