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T-joins intersecting small edge-cuts in graphs

✍ Scribed by Tomáš Kaiser; Riste Škrekovski

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
130 KB
Volume
56
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

In an earlier paper 3, we studied cycles in graphs that intersect all edge‐cuts of prescribed sizes. Passing to a more general setting, we examine the existence of T‐joins in grafts that intersect all edge‐cuts whose size is in a given set A ⊆{1,2,3}. In particular, we characterize all the contraction‐minimal grafts admitting no T‐joins that intersect all edge‐cuts of size 1 and 2. We also show that every 3‐edge‐connected graft admits a T‐join intersecting all 3‐edge‐cuts. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 64–71, 2007

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