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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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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Terminology for Maximal Subgraph without Bridges
Posted: Aug 24, 2013 3:33 AM
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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
> inclusion-maximal 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 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).

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 "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?

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.

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