Bounds on Maximum Weight Directed Cut
Combinatorics
2023-04-21 v1 Discrete Mathematics
Abstract
We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobas, Gyafas, Lehel and Scott (J Graph Th 55(1) (2007)) for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems.
Keywords
Cite
@article{arxiv.2304.10202,
title = {Bounds on Maximum Weight Directed Cut},
author = {Jiangdong Ai and Stefanie Gerke and Gregory Gutin and Anders Yeo and Yacong Zhou},
journal= {arXiv preprint arXiv:2304.10202},
year = {2023}
}