The 31st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2005) was held on the campus "Ile du Saulcy" of the Univ- sity Paul Verlaine-Metz in France. The workshop was organized by the La- ratoire d'Informatique Th' eorique et Appliqu' ee (LITA) and it took place June 23 - 25 2005. The 94 participants of WG 2005 came from universities and - search institutes of 18 di?erent countries. The WG 2005 workshop continues the series of 30 previous WG workshops. Since 1975,WG has taken place 20 times in Germany, four times in The Neth- lands,twotimesinAustriaaswellasonceinItaly,inSlovakia,inSwitzerlandand inCzechRepublic, andhas nowbeen heldfor the ?rsttime inFrance.The wo- shop aims at uniting theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas in computer science, or by extracting new problems from applications. The goal is to present recent research results and to identify and explore directions of future research. The talks were given in the "Petit Th' eatre". They showed how recent research results from algori- mic graph theory can be used in computer science and which graph-theoretic questions arise from new developments in computer science. There were two fascinating invited lectures by Georg Gottlob (Vienna, Austria) and Gregory Kucherov (Nancy, France).