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

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James Waldby

Posts: 545
Registered: 1/27/11
Re: Terminology for Maximal Subgraph without Bridges
Posted: Aug 24, 2013 10:44 AM
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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 inclusion-maximal 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 edge-connectivity, that is: a subset W of V is called a _???_ if W is inclusion-maximal 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 "bridge-block", 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 "link-connectivity-block" would be systematic, since it is about link-connectivity as opposed to vertex-connectivity as in the case of blocks. A short form would be "link-block".
> 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 co-opt the term "island", on the basis that island
sub-graphs are connected together by bridges. (I saw a web page
or article that used "island" for a less-well-defined 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".


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