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"Eulerian and Hamiltonian graphs" as a book-category would collect works focused on two central families of problems and concepts in graph theory: Eulerian graphs, which concern trails or circuits that use every edge exactly once (originating from Euler’s solution to the Königsberg bridges problem), and Hamiltonian graphs, which concern paths or cycles that visit every vertex exactly once (stemming from Hamilton’s Icosian Game). Titles in this category would range from introductory textbooks explaining definitions, classical characterizations and existence criteria, and constructive algorithms (e.g., Hierholzer’s and Fleury’s methods) to advanced monographs addressing sufficient conditions (Dirac, Ore, Bondy–Chvátal), computational complexity (NP-completeness of Hamiltonian problems), algorithmic heuristics and exact methods, and variations for directed, weighted, or constrained graphs. They would also cover applications — routing, DNA sequencing, network design, puzzles and games — as well as historical context, proof techniques, problem collections, and current research directions such as approximation algorithms and parameterized complexity.

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