This book constitutes the revised papers of the 45th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2019, held in Vall de Núria, Spain, in June 2019. The 29 full papers presented in this volume were carefully reviewed and selected from 87 submissions. They cover a wide range of areas, aiming at connecting theory and applications by demonstrating how graph-theoretic concepts can be applied in various areas of computer science. Another focus is on presenting recent results and on identifying and exploring promising directions of future research.