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Spiders can be Recognized by Counting Their Legs

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Abstract

Spiders are arthropods that can be distinguished from their closest relatives, the insects, by counting their legs. Spiders have eight, insects just six. Spider graphs are a very restricted class of graphs that naturally appear in the context of cograph editing. The vertex set of a spider (or its complement) is naturally partitioned into a clique (the body), an independent set (the legs), and a rest (serving as the head). Here we show that spiders can be recognized directly from their degree sequences through the number of their legs (vertices with degree 1). Furthermore, we completely characterize the degree sequences of spiders.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany

    Sarah J. Berkemer & Peter F. Stadler

  2. Bioinformatics Group, Department of Computer Science, Interdisciplinary Center for Bioinformatics, University of Leipzig, Härtelstrasse 16-18, 04107, Leipzig, Germany

    Sarah J. Berkemer & Peter F. Stadler

  3. Departamento de Ciência da Computação (CIC), Instituto de Ciências Exatas, Universidade de Brasília, Campus Universitário-Asa Norte, Brasília, DF, CEP 70910-900, Brazil

    Ricardo R. C. Chaves & Maribel Hernandez-Rosales

  4. Center for Bioinformatics, Saarland University, Building E 2.1, P.O. Box 15 11 50, 66041, Saarbrücken, Germany

    Adrian Fritz & Marc Hellmuth

  5. Department of Mathematics and Computer Science, Universityof Greifswald, Walther-Rathenau-Straße 47, 17487, Greifswald, Germany

    Marc Hellmuth

  6. Instituto de Matemáticas, UNAM Juriquilla, Blvd. Juriquilla 3001, Juriquilla, 76230, Santiago de Querétaro, QRO, Mexico

    Maribel Hernandez-Rosales

  7. RNomics Group, Fraunhofer Institut für Zelltherapie und Immunologie, Deutscher Platz 5e, 04103, Leipzig, Germany

    Peter F. Stadler

  8. Department of Theoretical Chemistry, University of Vienna, Währingerstraße 17, 1090, Vienna, Austria

    Peter F. Stadler

  9. Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM, 87501, USA

    Peter F. Stadler

Authors
  1. Sarah J. Berkemer
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  2. Ricardo R. C. Chaves
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  3. Adrian Fritz
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  4. Marc Hellmuth
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  5. Maribel Hernandez-Rosales
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  6. Peter F. Stadler
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Corresponding author

Correspondence to Marc Hellmuth.

Additional information

To all arachnophobic mathematicians.

This work was funded in part by the German Research Foundation (DFG) (Proj. No. MI439/14-1).

MHR is supported by the program “Cátedras Jóvenes Investigadores, CONACYT, México”.

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Berkemer, S.J., Chaves, R.R.C., Fritz, A. et al. Spiders can be Recognized by Counting Their Legs. Math.Comput.Sci. 9, 437–441 (2015). https://doi.org/10.1007/s11786-015-0233-1

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  • DOI: https://doi.org/10.1007/s11786-015-0233-1

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