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Cuts in matchings of 3-edge-connected cubic graphs. (arXiv:1712.06143v1 [math.CO])
来源于:arXiv
We discuss relations between several known (some false, some open)
conjectures on 3-edge-connected, cubic graphs and how they all fit into the
same framework related to cuts in matchings. We then provide a construction of
3-edge-connected digraphs satisfying the property that for every even subgraph
$E$, the graph obtained by contracting the edges of $E$ is not strongly
connected. This disproves a recent conjecture of Hochst\"attler [A flow theory
for the dichromatic number. European Journal of Combinatorics, 66, 160--167,
2017]. Furthermore, we show that an open conjecture of Neumann-Lara holds for
all planar graphs on at most 26 vertices. 查看全文>>