Definition: Saddle-ness is a concept in mathematics, specifically in graph theory, which refers to the property that every cycle in a graph can be decomposed into a path and an induced subgraph. In other words, if a graph has a cycle of length 4 (i.e., G = e1e2e3e4), then it is possible to construct two graphs, one with edges e1, e2, e3, and the other with edges e1, e2
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