Graph Theory: A Problem Oriented Approach by Daniel A. Marcus is a specialized textbook designed to teach graph theory through active problem-solving rather than passive reading. It is widely recognized for its "textbook-cum-workbook" format, which guides students through approximately 360-430 strategically placed problems that build concepts from the ground up. Core Methodology Active Involvement

: Instead of traditional long lectures, the book uses "leading questions" to help students discover definitions, theorems, and proofs on their own. : Each chapter is typically split into two groups: Main Problems

: Intended for third- and fourth-year math, computer science, and engineering majors, though the author famously states students just need to "bring their brains" as it starts from first principles. Key Topics Covered

The full text of the book can be found or previewed through various academic and public repositories: Graph Theory: A Problem Oriented Approach - AMS Bookstore

: Trees and forests, spanning tree algorithms, and bipartite graphs. Paths & Cycles : Euler paths, Hamilton paths, and Hamiltonian cycles. Coloring & Planarity : Vertex and edge coloring, and planar graphs. Advanced Topics

: Supplemental homework exercises (roughly 280-300 additional problems). Prerequisites

: New material introduced through connected problems and minimal bridging text. More Problems

The book covers essential graph theory topics in a logical, provocative sequence: Foundations : Basics, subgraphs, connectedness, and isomorphic graphs. Structures

: Matching theory, independence and covering, network flow theory, and cycle-free digraphs. American Mathematical Society Bookstore Accessing the PDF