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The Edge-Erdős-Pósa Property
Combinatorica ( IF 1.1 ) Pub Date : 2020-11-30 , DOI: 10.1007/s00493-020-4071-7
Henning Bruhn , Matthias Heinlein , Felix Joos

Robertson and Seymour proved that the family of all graphs containing a fixed graph H as a minor has the Erdős-Posa property if and only if H is planar. We show that this is no longer true for the edge version of the Erdős-Posa property, and indeed even fails when H is an arbitrary subcubic tree of large pathwidth or a long ladder. This answers a question of Raymond, Sau and Thilikos.

中文翻译:

The Edge-Erdős-Pósa 物业

Robertson 和 Seymour 证明了包含固定图 H 作为次要图的所有图的族具有 Erdős-Posa 性质当且仅当 H 是平面的。我们表明,这对于 Erdős-Posa 属性的边缘版本不再适用,甚至当 H 是大路径宽度或长梯子的任意亚立方树时甚至会失败。这回答了 Raymond、Sau 和 Thilikos 的问题。
更新日期:2020-11-30
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