Let $G$ be a graph with vertex set $[n]$. I say that a subset $S \subset [n]$ is a cut set of $G$ if $c(S \setminus \{i\}) Is something known about cut sets of a graph (maybe under a different name)? If so, what are good references for this? If I require that $G$ is bipartite and for every cut set $S$ of $G$, $c(S)=card(S)+1$, is it true that the intersection of any two cut sets is again a cut set? I know that the answer to the last question is negative if $G$ is not bipartite or the other condition does not hold. Thanks!
Vertex cutsets of a graph
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graph-theory
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0*Cut set* has the other [meaning][1] in graph theory. [1]: http://mathworld.wolfram.com/CutSet.html – 2017-01-23
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0Thanks for the remark. I'm probably referring to the something similar to vertex cutsets, with an additional condition on the number of connected components – 2017-01-23
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0It is not a vertex cut set, but a set of vertices each of which is a cutpoint of subgraph. Anyway you have well defined and seemingly new object. http://mathworld.wolfram.com/ArticulationVertex.html – 2017-01-24