Then, M is the double competition multigraph of an acyclic digraph if and only if there exist an ordering ([v.

Let M be the double competition multigraph of an acyclic digraph D.

If D is an acyclic digraph, then respecting intervals means preserving the partial order induced by D.

Then the relation induced on Q' by D is an acyclic digraph, which we denote by D' = D/~.

An activity network is an

acyclic digraph, where the vertices represent events, and the direct edges represent the activities, to be performed in a project [1,2].

The running of process phases is subject to precedence restrictions whose there is associated the

acyclic digraph G = (F,U), where if x, y [member of] F, then (x, y) [member of] U if and only if the beginning of the phase y need finishing of phase x.

The running of process phases is subject to precedence restrictions whose there is associated the

acyclic digraph G = (F, U), where if x, y [member of] F, then (x, y) [member of] U if and only if the beginning of the phase y need finishing of phase x.

is an

acyclic digraph with vertex set given by the blocks of [pi].

For illustration, recall that a vertex subset S [subset or equal to] V of a digraph G is a directed feedback vertex set, if removing S from G leaves an

acyclic digraph.

Roberts [12] observed that any graph G together with sufficiently many isolated vertices is the competition graph of an

acyclic digraph.

Indeed, a network whose underlying interaction graph is an

acyclic digraph can only eventually end up in a configuration that will never change over time (aka.

Graphs with no PEC cycles or closed trails are interesting since they constitute, in a certain sense, the edge-colored counterpart of non-colored

acyclic digraphs.