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\((-1)\)-Hypomorphic Graphs with the Same 3-Element Homogeneous Subsets

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Abstract

A 3-element homogeneous subset of a graph G is a 3-element subset of the vertex set of G which forms a clique or an independent set. We prove that Ulam Reconstruction Conjecture is true for pairs of graphs having the same 3-element homogeneous subsets. This new approach in graph reconstruction is motivated by a result, obtained in 2011 by Pouzet, Si Kaddour and Trotignon, giving a description of the boolean sum \(G\dot{+} G'\) of two graphs G and \(G'\) having the same 3-element homogeneous subsets.

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Acknowledgements

We are pleased to thank the referee for his constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, B.P. 802, 3018, Sfax, Tunisia

    Jamel Dammak

  2. Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, Univ Lyon, 43 blvd. du 11 novembre 1918, 69622, Villeurbanne cedex, France

    Hamza Si Kaddour

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  1. Jamel Dammak
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  2. Hamza Si Kaddour
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Correspondence to Hamza Si Kaddour.

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Dammak, J., Si Kaddour, H. \((-1)\)-Hypomorphic Graphs with the Same 3-Element Homogeneous Subsets. Graphs and Combinatorics 35, 427–436 (2019). https://doi.org/10.1007/s00373-018-02005-y

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  • DOI: https://doi.org/10.1007/s00373-018-02005-y

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