Graph Colouring, Graph Clique, Algorithms and Applications

This thesis deals with the problem of graph coloring and finding cliques in a graph, with a focus on the description of algorithms and their applications. Graph coloring is the process of assigning colors to individual vertices of a graph so that adjacent vertices have different colors. This issue is important for solving various optimization problems. The work also focuses on finding cliques in a graph, which is an important problem in social network analysis or image recognition. The aim of this thesis is to provide a complex overview of graph coloring, finding cliques in a graph, introduce and analyze existing algorithms and show their applications in practice