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edge-connectivity
Kriesell's Conjecture ★★
Author(s): Kriesell
Conjecture Let
be a graph and let
such that for any pair
there are
edge-disjoint paths from
to
in
. Then
contains
edge-disjoint trees, each of which contains
.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ T\subseteq V(G) $](/files/tex/0acf1a8ecf3a0737d34c34b8652d10a2c33df19b.png)
![$ u,v\in T $](/files/tex/bbcef09f86563651f02daa6bbae826055f48edfb.png)
![$ 2k $](/files/tex/bded1a5bf39ed2baaf98bd8c04cea4667dd89b58.png)
![$ u $](/files/tex/06183efdad837019eb0937c4e40f9e7beaa2e8d8.png)
![$ v $](/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ T $](/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png)
Keywords: Disjoint paths; edge-connectivity; spanning trees
Partitioning edge-connectivity ★★
Author(s): DeVos
Question Let
be an
-edge-connected graph. Does there exist a partition
of
so that
is
-edge-connected and
is
-edge-connected?
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ (a+b+2) $](/files/tex/af1c5eba58500364df6ff49bb0249ecfe43563fb.png)
![$ \{A,B\} $](/files/tex/b4558816c01c418eea76d970f1e3afdfd18e42d8.png)
![$ E(G) $](/files/tex/4b556e49b77160d4c8a0131e0efdfefd52dda2bb.png)
![$ (V,A) $](/files/tex/0682e0dcb16e4b0bfdebe28127ce935ebf4f792e.png)
![$ a $](/files/tex/b1d91efbd5571a84788303f1137fb33fe82c43e2.png)
![$ (V,B) $](/files/tex/a79aaba9b9fa199ba406f5d713827cda8507ed7c.png)
![$ b $](/files/tex/b94226d9717591da8122ae1467eda72a0f35d810.png)
Keywords: edge-coloring; edge-connectivity
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