Eulerian Cycles and Paths in Graph Theory and Bioinformatics

Graph theory provides the mathematical backbone for solving some of modern science's most complex challenges, including reconstructing DNA sequences. This text-based course guides you through the foundational concepts of Eulerian paths and cycles, showing you how theoretical mathematics directly applies to computational biology. You will transition from understanding basic graph structures to writing clear algorithms that solve complex routing and assembly problems. What you'll learn: - Understand the core terminology of graph theory, including vertices, edges, degrees, and directed graphs - Analyze Euler's Theorem to determine when an Eulerian path or cycle exists in a given graph - Construct Eulerian cycles and paths step-by-step using classical graph traversal algorithms - Apply Eulerian path concepts to the de Bruijn graph approach used in modern genome assembly - Practice dry-running algorithms with written tracing exercises to solidify your logical understanding This course begins with essential definitions and foundational theorems before introducing the algorithms used to construct paths. You will then explore how these mathematical principles are applied to assemble genomes from short DNA reads. Written for beginners, this course requires no prior background in advanced mathematics or biology. Start reading today to unlock the power of graph theory in bioinformatics.