
Re: Terminology for Maximal Subgraph without Bridges
Posted:
Aug 24, 2013 3:33 AM


On Fri, 23 Aug 2013, Lasse Kliemann wrote:
> Let G=(V,E) be a graph. Then a subset B of V is called a _block_ if B is > inclusionmaximal under the condition that G[B] (i.e., the subgraph induced > by B) does not contain any articulations of G[B]. > What's an articulation?
> What about the analog for edgeconnectivity, that is: a subset W of V is > called a _???_ if W is inclusionmaximal under the condition that G[W] does > not contain any bridges of G[W] (or, equivalently, does not contain any > bridges of G).
What's a bridge?
> In a very few places in the literature, the latter is also called "block", > which I do not agree with since it can cause confusion. In another place, it > is called "bridgeblock", which I also find confusing since it is about > subgraphs *without* bridges. I used to use "bridgeless connected component" > in my own texts, but am not convinced of it anymore. > > Perhaps "linkconnectivityblock" would be systematic, since it is about > linkconnectivity as opposed to vertexconnectivity as in the case of > blocks. A short form would be "linkblock". > > Another direction of thought would look for similar words to "block", such > as "chunk", "section", "group", "part", etc.
> None of that convinces me right now. Any suggestions? Lot, clump, lump.
> Note that the set of the <whatever we call it> forms a partition of the > vertex set, as opposed to blocks (which may share articulations). This > enticed me once to call them "components". But this can be confused with > connected components.

