Ứng dụng một số lớp đồ thị trong nội dung môn toán dành cho lớp chuyên vào việc giải một số bài toán trong các kỳ thi học sinh giỏi

Abstract

This paper presents the application of fundamental graph classes to solving problems in the mathematics curriculum for gifted students and mathematical olympiads. A procedure is set to model elementary problems as graph problems, thereby leveraging graph theorems and characteristic properties to derive solutions that are both concise and creative. This paper illustrates this procedure through specific examples, including problems selected from the VMO and IMO. The main contribution of this paper is to clarify a three - step procedure and the process of transforming between languages to solve a specific mathematical problem, thereby highlighting the direct applicability in teaching, in contrast to previous studies that primarily focus on theoretical aspects. Consequently, it contributes to enhancing teachers' and students' insight into the role of graph theory in fostering gifted mathematics students.