Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656690 | Journal of Combinatorial Theory, Series B | 2016 | 19 Pages |
Abstract
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=3k=3 is equivalent to the Four Color Theorem, and the cases k=4k=4, which was conjectured by Seymour, and k=5k=5 were proved by Guenin. We settle the next open case k=6k=6.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Zdeněk Dvořák, Ken-ichi Kawarabayashi, Daniel Král',