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The 31st International Workshop on GraphTheoretic Concepts in Computer Science (WG 2005) was held on the campus 'Ile du Saulcy' of the Univ sity Paul VerlaineMetz 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 graphtheoretic 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 graphtheoretic questions arise from new developments in computer science. There were two fascinating invited lectures by Georg Gottlob (Vienna, Austria) and Gregory Kucherov (Nancy, France).
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