Packing six T-joins in plane graphs

Details Packing six T-joins in plane graphs Packing six T-joins in plane graphs

2010-09-29

arxiv.org/abs/1009.5912v1

Mathematics

Combinatorics

Scientific paper

Let G be a plane graph and T an even subset of its vertices. It has been
conjectured that if all T-cuts of G have the same parity and the size of every
T-cut is at least k, then G contains k edge-disjoint T-joins. The case k=3 is
equivalent to the Four Color Theorem, and the cases k=4, which was conjectured
by Seymour, and k=5 were proved by Guenin. We settle the next open case k=6.

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