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Rainbow matchings in bipartite multigraphs

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Abstract

Suppose that k is a non-negative integer and a bipartite multigraph G is the union of

$$\begin{aligned} N=\left\lfloor \frac{k+2}{k+1}n\right\rfloor -(k+1) \end{aligned}$$

matchings \(M_1,\dots ,M_N\), each of size n. We show that G has a rainbow matching of size \(n-k\), i.e. a matching of size \(n-k\) with all edges coming from different \(M_i\)’s. Several choices of the parameter k relate to known results and conjectures.

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Acknowledgements

A. Gyárfás: Research was supported in part by OTKA K104343. G. N. Sárközy: Research was supported in part by OTKA K104343.

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Authors and Affiliations

  1. MTA-ELTE Geometric and Algebraic Combinatorics Research Group, Budapest, Hungary

    János Barát

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, Budapest, 1364, Hungary

    András Gyárfás & Gábor N. Sárközy

  3. Computer Science Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Gábor N. Sárközy

Authors
  1. János Barát
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  2. András Gyárfás
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  3. Gábor N. Sárközy
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Correspondence to András Gyárfás.

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Barát, J., Gyárfás, A. & Sárközy, G.N. Rainbow matchings in bipartite multigraphs. Period Math Hung 74, 108–111 (2017). https://doi.org/10.1007/s10998-016-0172-x

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