on cut edges and bonds, graph theory

From	Daniel Bastos <dbastos@toledo.com>
Newsgroups	comp.programming, alt.algebra.help
Subject	on cut edges and bonds, graph theory
Date	2017-09-18 12:51 -0300
Organization	Aioe.org NNTP Server
Message-ID	<86wp4w3sz5.fsf@toledo.com> (permalink)

Cross-posted to 2 groups.

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This is a question on the definition of cut edges, edge cuts and bonds
as given by section 2.2, page 27-29 of

  ``Graph theory with applications'' by J.A. Bondy and U.S.R. Murty,
  Department of Combinatorics and Optimization, University of Waterloo,
  Ontario, Canada.  North-Holland, fifth printing, 1982.  ISBN:
  0-444-19451-7.

I understand cut edges.  It's defined in page 27.

Definition (cut edge).  A cut edge of G is an edge e such that 
w(G - e) > w(G), where w(G) means the number of components of G.

It says e is a a cut edge if removing e from G yields more components
than we had before.  In other words, e is necessary to keep G with the
components it had.  (In particular, if G is connected, then e is
necessary to keep G connected.)

No problem here.

On page 29, edge cuts are defined.  (My writing.)

Notation (separation).  For subsets S and S' of V, we denote [S, S'] the
set of edges with one end in S and the other in S'.

Question.  It seems [S, S'] is a separation of G into two parts.  Does
it mean [S,S'] contains all possible (x,y) edges for x in S, y in S'?

Although the book gave me Figure 2.4 (a), it didn't give me S and S', so
I'm not sure which vertices of the picture would be in S.

Thank you!

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on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-18 12:51 -0300
  Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-18 20:40 +0100
    Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-18 21:39 -0700
      Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-19 13:05 +0100
        Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-19 19:47 -0700
          Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-20 14:28 +0100
            Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-20 21:06 -0700
              Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-21 17:03 +0100
                Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-21 15:06 -0300
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-21 21:24 +0100
                Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-21 17:57 -0300
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-21 23:40 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-21 20:45 -0700
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-23 02:27 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-22 19:49 -0700
                Re: on cut edges and bonds, graph theory Richard Heathfield <rjh@cpax.org.uk> - 2017-09-23 08:04 +0100
                Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-23 08:41 -0300
                Re: on cut edges and bonds, graph theory Paul N <gw7rib@aol.com> - 2017-09-24 14:00 -0700
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-23 14:50 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-23 22:04 -0700
                Re: on cut edges and bonds, graph theory Richard Heathfield <rjh@cpax.org.uk> - 2017-09-24 07:39 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-25 01:13 -0700
                Re: on cut edges and bonds, graph theory Richard Heathfield <rjh@cpax.org.uk> - 2017-09-25 09:46 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-25 21:38 -0700
                Re: on cut edges and bonds, graph theory Richard Heathfield <rjh@cpax.org.uk> - 2017-09-26 10:19 +0100
                Modern Trash William Elliot <marsh@panix.com> - 2017-09-26 03:37 -0700
                Re: Modern Trash David Brown <david.brown@hesbynett.no> - 2017-09-26 12:52 +0200
                Re: Modern Trash Richard Heathfield <rjh@cpax.org.uk> - 2017-09-26 23:10 +0100
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-24 22:33 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-25 01:08 -0700
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-25 20:44 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-25 21:36 -0700
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-26 12:04 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-26 23:15 -0700
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-27 12:52 +0100
                Re: on cut edges and bonds, graph theory William Elliot <marsh@panix.com> - 2017-09-27 19:55 -0700
                Re: on cut edges and bonds, graph theory Ike Naar <ike@iceland.freeshell.org> - 2017-09-24 16:55 +0000
        Re: on cut edges and bonds, graph theory David Brown <david.brown@hesbynett.no> - 2017-09-22 10:23 +0200
          Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-22 21:18 +0100
            Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-23 08:48 -0300
            Re: on cut edges and bonds, graph theory David Brown <david.brown@hesbynett.no> - 2017-09-25 10:17 +0200
              Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-25 07:31 -0300
                Re: on cut edges and bonds, graph theory David Brown <david.brown@hesbynett.no> - 2017-09-25 13:30 +0200
              Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-25 20:32 +0100
                Re: on cut edges and bonds, graph theory David Brown <david.brown@hesbynett.no> - 2017-09-26 10:12 +0200
                Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-26 11:53 +0100
                Re: on cut edges and bonds, graph theory David Brown <david.brown@hesbynett.no> - 2017-09-26 13:24 +0200
    Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-19 16:21 -0300
      Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-20 17:43 +0100
        Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-21 16:20 -0300
          Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-21 17:52 -0300
          Re: on cut edges and bonds, graph theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-09-21 22:02 +0100
            Re: on cut edges and bonds, graph theory Daniel Bastos <dbastos@toledo.com> - 2017-09-23 13:42 -0300

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