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On Zero-Sum and Almost Zero-Sum Subgraphs Over \({\mathbb {Z}}\)

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Abstract

For a graph \(H\) with at most \(n\) vertices and a weighing of the edges of \(K_n\) with integers, we seek a copy of \(H\) in \(K_n\) whose weight is minimal, possibly even zero. Of a particular interest are the cases where \(H\) is a spanning subgraph (or an almost spanning subgraph) and the case where \(H\) is a fixed graph. In particular, we show that relatively balanced weighings of \(K_n\) with \(\{-r,\ldots ,r\}\) guarantee almost zero-sum copies of spanning graphs with small maximum degree, guarantee zero-sum almost \(H\)-factors, and guarantee zero-sum copies of certain fixed graphs.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa at Oranim, 36006, Tivon, Israel

    Yair Caro

  2. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Raphael Yuster

Authors
  1. Yair Caro
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  2. Raphael Yuster
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Correspondence to Raphael Yuster.

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Caro, Y., Yuster, R. On Zero-Sum and Almost Zero-Sum Subgraphs Over \({\mathbb {Z}}\) . Graphs and Combinatorics 32, 49–63 (2016). https://doi.org/10.1007/s00373-015-1541-6

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  • DOI: https://doi.org/10.1007/s00373-015-1541-6

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