Teorija grafova i zadaci s natjecanja

U ovom radu je dan kratak uvid u razvoj teorije grafova s naglaskom na poznati problem teorije grafova - problem Königsberških mostova. Nakon povijesnog pregleda razvoja teorije grafova te definicije pojma graf u radu se baziramo na osnovne pojmove vezane uz grafove kao što su stupanj vrha, poveznost vrhova u grafu, dokazujemo Lemu o rukovanju te su navedeni i riješeni zadaci vezani uz to područje teorije grafova. Zadnji dio rada posvećen je obilascima grafa, odnosno postojanju Eulerove ture. Rješenje problema Königsberških mostova generalizirano je Eulerovim teoremom.This paper provides a brief overview of the development of graph theory with a focus on the well-known problem of graph theory - Königsberg bridge problem. Following historical review of development of graph theory and definition of the term graph, this paper is focused on basic concepts related to graphs such as degree of a vertex, connections between vertices in the graph, we prove the handshaking lemma on the operation and there are given and solved problems related to the area of graph theory. The last part is dedicated to the trail in the graph and the existence of Eulerian cycle. Solution to Königsberg bridge problem is generalized with Euler’s theorem