Yet, another example is the problem of arranging guests attending a wedding aroundtables. Given a list of “irreconcilable differences” between invitees, you task is to find aseating arrangement that uses the least number of tables while avoiding to have twoindividuals with “irreconcilable differences” sitting around the same table. This is agraph coloring problem! Namely, we can solve the problem by (1) modeling eachindividual as a vertex in a graph, (2) representing the fact that two individuals haveirreconcilable differences by drawing an edge between the vertices corresponding tothi di idld (3)i ii ithbfl(t bl)d tlththese individuals, and (3) minimizing the number of colors (tables) used to color thevertices (seat the guests) such that no two vertices connected with an edge (two guestswith irreconcilable differences) have the same color (are sitting on the same table).Along the same lines, one can use graph vertex coloring to solve other (quiteimportant) problems, including assigning the minimum number of radio frequencies tovarious radio transmitters who may interfere with one another – here the radio stationsvarious radio transmitters who may interfere with one anotherhere the radio stationswould be the vertices, and if two stations interfere with one another (because ofgeographical proximity) then we draw an edge between them. Now coloring the graphis akin to assigning frequencies since we would not want to give the same frequency(color) to interfering stations (adjacent vertices).Yet, another famous application of graph coloring is “map coloring”. Here our job is tocolor adjacent states (vertices) on a planar map (e.g., map of the US) with differentcolors , but use the minimum number of colors. This fairly classical problem was settledby proving that one need no more than 4 colors for such (planar) graphs.3
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