$T$-Joins in Infinite Graphs
نویسندگان
چکیده
منابع مشابه
$T$-Joins in Infinite Graphs
We characterize the class of infinite connected graphs G for which there exists a T -join for any choice of an infinite T ⊆ V (G). We also show that the following well-known fact remains true in the infinite case. If G is connected and does not contain a T -join, then it will if we either remove an arbitrary vertex from T or add any new vertex to T .
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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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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/6308