The concept of an answer set (or stable model) was originally proposed as a theory of the negation as failure operator in the logic programming language Prolog. In recent years, the invention of efficient algorithms for computing answer sets has led to the emergence of a new approach to solving combinatorial search problems, called answer set programming. Its idea is to represent the given problem as a logic program whose answer sets correspond to solutions, and then find a solution using a system for computing answer sets. In this talk we will show how some concepts of graph theory can be described in terms of answer sets.