A Cactus Theorem for End Cuts

@article{Evangelidou2011ACT,
  title={A Cactus Theorem for End Cuts},
  author={Anastasia Evangelidou and Panos Papasoglu},
  journal={IJAC},
  year={2011},
  volume={24},
  pages={95-}
}
Dinits–Karzanov–Lomonosov showed that it is possible to encode all minimal edge cuts of a graph by a tree-like structure called a cactus. We show here that minimal edge cuts separating ends of the graph rather than vertices can be "encoded" also by a cactus. As a corollary, we obtain a new proof of Stallings' ends theorem. We apply our methods to finite graphs as well and we show that several types of cuts can be encoded by cacti. 

Figures and Topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.
SHOWING 1-4 OF 4 CITATIONS

On the structure of vertex cuts separating the ends of a graph

VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Gomory-Hu trees of infinite graphs with finite total weight

  • Journal of Graph Theory
  • 2017
VIEW 1 EXCERPT
CITES BACKGROUND

Cutting up graphs revisited – a short proof of Stallings' structure theorem

  • Groups Complexity Cryptology
  • 2010
VIEW 1 EXCERPT
CITES BACKGROUND