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This textbook is built from a semester-long lecture series delivered by the author to first-year bachelor’s students at the St. Petersburg Academic University. It covers the essential sections of modern graph theory, including trees, cycles, connectivity in graphs, matchings, graph colorings, and planar graphs. Each paragraph concludes with problems that complement the theoretical material presented in the textbook. All statements are accompanied by detailed proofs, and the exposition is illustrated with a large number of figures.
The textbook is designed for undergraduate students studying mathematics and computer science, as well as for specialists in related fields who wish to independently study the basic sections of graph theory. Most of the material does not require specialized prior knowledge and can be used by school students studying programming and discrete mathematics. Finally, this textbook may be useful for instructors teaching relevant courses.