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At the opposite extreme is the class of graphs for which the threshold weight is the maximum possible. Such graphs are defined as <jats:italic>heavy graphs.<\/jats:italic> Among the results are as following: A theorem that specifies the threshold weight of any triangle\u2010free graph; necessary and sufficient conditions for a heavy graph in terms of the solvability of a system of linear inequalities; some sufficient conditions for a graph to be heavy and a necessary condition (conjectured to be sufficient, as well) for a heavy graph in terms of its cliques.<\/jats:p>","DOI":"10.1002\/jgt.3190150302","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T07:49:07Z","timestamp":1181288947000},"page":"235-249","source":"Crossref","is-referenced-by-count":3,"title":["The threshold weight of a graph"],"prefix":"10.1002","volume":"15","author":[{"given":"Chi","family":"Wang","sequence":"first","affiliation":[]},{"given":"A. 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