Abstract

Abstract We present one more proof of the fact that the class of proper interval graphs is precisely the class of unit interval graphs. The proof leads to a new and efficient O ( n ) time and space algorithm that transforms a proper interval model of the graph into a unit model, where all the extremes are integers in the range 0 to O ( n 2 ) , solving a problem posed by Gardi (Discrete Math., 307 (22), 2906–2908, 2007).

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