this book constitutes the refereed proceedings of the 25th international workshop on graph-theorie concepts in computer science wg99, held at the centre stefano frascini on monte verita, ascona, switzerland in june 1999. the 33 revised full papers presented together with four invited contributions were carefully reviewed and selected from 64 papers submitted. the papers provide a wealth of new results for various graph classes, graph computations, graph algorithms and graph-theoretical applications in a variety of fields.