Algorithms and Applications
Some facility location problems which are NP-hard for general graphs, as well as some other graph problems, may be solved in polynomial time for cacti.
Since cacti are special cases of outerplanar graphs, a number of combinatorial optimization problems on graphs may be solved for them in polynomial time.
Cacti represent electrical circuits that have useful properties. An early application of cacti was associated with the representation of op-amps.
Cacti have also recently been used in comparative genomics as a way of representing the relationship between different genomes or parts of genomes.
If a cactus is connected, and each of its vertices belongs to at most two blocks, then it is called a Christmas cactus. Every polyhedral graph has a Christmas cactus subgraph that includes all of its vertices, a fact that plays an essential role in a proof by Moitra & Leighton (2008) that every polyhedral graph may be embedded in the plane in such a way that greedy forwarding succeeds in routing messages between all pairs of vertices.
Read more about this topic: Cactus Graph