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Topic:
Terminology for Maximal Subgraph without Bridges
Replies:
4
Last Post:
Aug 25, 2013 1:38 PM




Re: Terminology for Maximal Subgraph without Bridges
Posted:
Aug 24, 2013 10:44 AM


On Fri, 23 Aug 2013 05:24:34 0700, Lasse Kliemann wrote:
> I'd like to discuss some graph theory terminology. > > 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 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). > > 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? ...
You might coopt the term "island", on the basis that island subgraphs are connected together by bridges. (I saw a web page or article that used "island" for a lesswelldefined idea, that of dividing nodes into clusters based on a high ratio of number of edges within the cluster vs edges entering or leaving.) An alternative to "island" is "mass".
 jiw



