Book

Description

How can every edge of a graph be arranged into five-edge cycles, with each edge used exactly once? This question leads us to a conjecture, where a simple statement opens into a demanding mathematical problem. In Exploring a Conjecture of Maryam Mirzakhani, we begin with the ideas behind the problem and develop the arithmetic, constructions and proof techniques needed to study particular families of complete tripartite graphs. Worked examples and figures make the arguments easier to follow, while computational tools connect the reasoning on the page with explicit checks. We also remember Mirzakhani’s life and mathematical journey. Her patience with difficult questions is close to the spirit in which we have written this book: to understand a problem carefully, to make each step clear, and to keep searching when the next step is uncertain. Written for students, researchers, and readers with an interest in discrete mathematics, this book invites a close encounter with the work of mathematical discovery.