A Practical and Pedagogical Demonstration of the Tutte-Berge and Tutte Theorems
DOI:
https://doi.org/10.20873/uft.2675-3588.2026.v7n2.p41-50Keywords:
Graph Theory, Tutte-Berge Theorem, Tutte’s Theorem, Maximum Matchings, Barriers, Academic Seminars, Pedagogical ExperienceAbstract
This paper reports on a pedagogical experience developed during the Graph Theory course within the Computer Science program, offered in the second semester of 2025 at the Federal University of Tocantins. The practical application of the graph concepts learned in the course involves reproducing the proofs of the Tutte-Berge and Tutte theorems, which represented major advancements in graph matching research. More specifically, it focuses on the study of the existence conditions for maximum and perfect matchings in arbitrary graphs. These studies, in turn, paved the way for solving increasingly complex problems, and the versatility of their applications can be interpreted as a complement to the achievements brought by Hall's Theorem. The explanation of these concepts is based on the primary difficulties encountered by the student body, employing a didactic approach illustrated with images to reduce the inherent abstraction of the subject matter.
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Copyright (c) 2026 João Pedro Felix Veloso, Artur Anderson Alves Corrêa, Daniel Martins da Silva, Tanilson Dias dos Santos
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