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Weighted Rooted Trees: Fat or Tall?

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Computer Science – Theory and Applications (CSR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12159))

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Abstract

Let V be a countable set, let T be a rooted tree on the vertex set V, and let \({\mathcal M}=(V,2^V, \mu )\) be a finite signed measure space. How can we describe the “shape” of the weighted rooted tree \((T, {\mathcal M})\)? Is there a natural criterion for calling it “fat” or “tall”? We provide a series of such criteria and show that every “heavy” weighted rooted tree is either fat or tall, as we wish. This leads us to seek hypergraphs such that regardless of how we assign a finite signed measure on their vertex sets, the resulting weighted hypergraphs have either a “heavy” large matching or a “heavy” vertex subset that induces a subhypergraph with small matching number. Here we also must develop an appropriate definition of what it means for a set to be heavy in a signed measure space.

Supported by NSFC (11671258, 11971305) and STCSM (17690740800).

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Notes

  1. 1.

    More precisely, an Alexandroff space is the set of down-sets of a preorder.

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Authors and Affiliations

  1. School of Mathematical Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yaokun Wu & Yinfeng Zhu

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  1. Yaokun Wu
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  2. Yinfeng Zhu
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Correspondence to Yinfeng Zhu .

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Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

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Wu, Y., Zhu, Y. (2020). Weighted Rooted Trees: Fat or Tall?. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_30

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  • DOI: https://doi.org/10.1007/978-3-030-50026-9_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-50025-2

  • Online ISBN: 978-3-030-50026-9

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