We introduce interval number and boxicity for digraphs, analogous to the corresponding concepts for graphs. The results are: 1) i(D) maxf + (D); ? (D)g, which is sharp. 2) The largest interval number of an n-vertex digraph is between (1?o(1)) n 4lg 2n and n lg n + 2. 3) The largest boxicity of an n-vertex digraph is dn=2e.

Article history: Received 17 January 2008 Available online 14 March 2009 Communicated by F. Dehne

An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...

The interval number of a graph G is the least natural number t such that G is the intersection graph of sets, each of which is the union of at most t intervals, denoted by i (G ). Griggs and West showed that i(G) d12(d þ 1)e. We describe the extremal graphs for that inequality when d is even. For three special perfect graph classes we give bounds on the interval number in terms of the independe...