Properties
Cacti are outerplanar graphs. Every pseudotree is a cactus. A graph is a cactus if and only if every block is either a simple cycle or a single edge.
The family of graphs in which each component is a cactus is downwardly closed under graph minor operations. This graph family may be characterized by a single forbidden minor, the four-vertex diamond graph formed by removing an edge from the complete graph K4.
Read more about this topic: Cactus Graph
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—John Locke (1632–1704)
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