Dedicated to Stephen Simons on the occasion of his 70 th birthday We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most single-valued operators by Phelps and Simons and by Bauschke, Borwein and Wang. Furthermore, a description of skew linear relations in terms of the Fitzpatrick family is obtained. We also answer one of Simons ’ problems by showing that if a maximal monotone operator has a convex graph, then this graph must actually be affine. 2000 Mathematics Subject Classification
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