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Maximum directed cuts in acyclic digraphs Bela Bollobas

Summary: Maximum directed cuts in acyclic digraphs
Noga Alon
B´ela Bollob´as
Andr´as Gy´arf´as
Jeno Lehel §
Alex Scott ¶
June 27, 2007
It is easily shown that every digraph with m edges has a directed cut of
size at least m/4, and that 1/4 cannot be replaced by any larger constant.
We investigate the size of a largest directed cut in acyclic digraphs, and
prove a number of related results concerning cuts in digraphs and acyclic
1 Introduction
Results on maximum cuts in an undirected graph have a huge literature (see
Poljak and Tuza [21] and Laurent [19]), and the extremal Max Cut problem is
now quite well understood. Given a graph and a partition of its vertex set into
sets X, Y , a cut (X, Y ) means the edge set E(X, Y ) with one endpoint in X
and the other endpoint in Y . The size of the cut (X, Y ) is e(X, Y ) = |E(X, Y )|.
Similarly, we write e(X) for the number of edges with both ends in X. For


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics