Graph Theory with Applications in Games and Other Real Problems

V diplomskem delu so opisane miselne igre, katerih rešitve lahko naravno podamo s pomočjo teorije grafov. Pogledamo nekaj najbolj znanih zagonetk in jih predstavimo v obliki dobro raziskanih ter znanih grafov. Ti med drugimi vključujejo polne dvodelne grafe, hiperkocke in zgodovinsko znan graf Königsbergških mostov. Vpeljemo možno posplošitev zagonetk na poljubno dimenzijo in podamo zmagovalno strategijo. V delu se podrobneje obravnavajo tudi določeni gospodarski problemi in uporaba teorije grafov v realnem svetu na različnih področjih kot so optimizacijski problemi, minimiziranje cene v ekonomiji, problemi v prometu in teoriji koristnosti. Postavimo vprašanje, ali ima izbran problem sprejemljivo rešitev in če je možno, predlagamo algoritem, ki privede do rešitve.In the following thesis we describe a set of playable mind games that lend themselves to an elegant transfiguring in the form of a graph. By means of graph theory, we are able to convert some of the most well-known brain teasers and re-imagine them as famous graphs. These among others include bipartite graphs, hypercubes and a historically famous Königsberg bridge graph. We provide the means of generalizing the aforementioned games to an arbitrary dimension, and also contribute a winning strategy in conceived situations. We take a closer look at the application of graph theory to solving real-world problems in fields ranging from route optimization, cost reductions, to tra c and utility related problems. If an e cient solution for a given problem exists, we suggest an algorithm that confers a solution