Graph Theory for Genome Assembly: Euler, Hamilton, and de Bruijn

How do scientists reconstruct an entire genome from billions of tiny, scattered DNA fragments? The answer lies not just in biology, but in elegant graph theory concepts developed over centuries. This text-based course guides you through the mathematical foundations of genome assembly, showing you exactly how Eulerian paths, Hamiltonian cycles, and de Bruijn graphs form the backbone of modern bioinformatics. By reading through clear explanations and structured examples, you will learn to conceptualize biological data as mathematical networks and understand how assembly algorithms piece genetic puzzles together. What you'll learn: - Understand the foundational principles of graph theory, including nodes, edges, and directed networks. - Compare Hamiltonian and Eulerian paths to see why genome assembly transitioned from one approach to the other. - Construct de Bruijn graphs conceptually from k-mers to represent overlapping DNA sequences. - Identify common assembly challenges, such as genomic repeats and sequencing errors, and how modern algorithms resolve them. - Analyze how next-generation sequencing data is processed using graph-based computational models. We begin with basic terminology and historical mathematical puzzles before moving into practical algorithmic applications. Through clear written explanations and step-by-step conceptual walkthroughs, you will trace how raw sequence reads are transformed into complete genomic maps. This course is designed for beginners in bioinformatics, computer science, or biology with no prior advanced mathematics background. Start reading today to bridge the gap between discrete mathematics and genomic discovery.