Nets, Puzzles and Postmen

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What do road and railway systems, mingling at parties, mazes, family trees, and the internet have in common? They are all networks—entities that connect and relate to one another. In this engaging exploration, Peter Higgins reveals that these diverse phenomena share a deep mathematical structure. The mathematics of networks underpins intriguing puzzles and problems, from tic-tac-toe to circular sudoku. By understanding networks, we gain remarkable insights into these puzzles and a variety of real-world issues. Higgins offers fresh perspectives on well-known mathematical challenges, such as the four-color map and the bridges of Konisberg, while posing intriguing questions like whether you can walk through all the doors of a house just once. He also delves into the Postman Problem, which seeks the most efficient way to deliver letters and return to the starting point without retracing any streets. Additionally, he examines the Harem Problem, a variation of the Marriage Problem, focused on satisfying the preferences of men seeking multiple wives. Recently, mathematicians have begun to uncover the significance of networks and connections, leading to surprising discoveries. This captivating journey into the world of networks will delight math enthusiasts everywhere.