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janvdl
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Do these go by any other name? I'm really struggling to find information on them. So far I've found a paper on it by Chartrand & Lesniak. (Dull)
janvdl said:Do these go by any other name? I'm really struggling to find information on them. So far I've found a paper on it by Chartrand & Lesniak. (Dull)
A recognizable coloring of a graph is a way to assign colors to the vertices of a graph such that no two adjacent vertices have the same color. This is also known as a proper coloring.
A recognizable coloring is a special type of regular coloring where the colors used are restricted to a specific set. For example, a recognizable coloring of a graph with 4 vertices will use only 4 distinct colors.
Recognizable colorings have numerous applications in fields such as computer science, chemistry, and biology. In computer science, they are used in graph coloring problems and scheduling algorithms. In chemistry, they can represent the bonding patterns of molecules. In biology, they can represent the genetic relationships between organisms.
The concept of recognizable colorings is a fundamental concept in graph theory. It is closely related to the concepts of vertex coloring and chromatic number, which are important in studying the structure and properties of graphs.
No, not all graphs have recognizable colorings. For example, a complete graph with an odd number of vertices does not have a recognizable coloring. However, for most graphs, it is possible to find a recognizable coloring with the right number of colors. The minimum number of colors needed for a recognizable coloring is known as the chromatic number of a graph.