Advertisement

Mathematics in Computer Science

, Volume 9, Issue 4, pp 437–441 | Cite as

Spiders can be Recognized by Counting Their Legs

  • Sarah J. Berkemer
  • Ricardo R. C. Chaves
  • Adrian Fritz
  • Marc HellmuthEmail author
  • Maribel Hernandez-Rosales
  • Peter F. Stadler
Article
  • 206 Downloads

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.

Keywords

Phylogenetics Cograph P4-sparse Spider Degree sequence 

Mathematics Subject Classification

Primary 05C07 Secondary 05C75 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Erdős P., Gallai T.: Gráfok előírt fokszámú pontokkal. Mat. Lapok 11, 264–274 (1960)Google Scholar
  2. 2.
    Hakimi S.L.: On realizability of a set of integers as degrees of the vertices of a linear graph. J. Soc. Ind. Appl. Math. 10, 496–506 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Havel V.: A remark on the existence of finite graphs. Časopis Pro pěstování Matematiky (in Czech) 80, 477–480 (1955)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Hellmuth M., Hernandez-Rosales M., Huber K.T., Moulton V., Stadler P.F., Wieseke N.: Orthology relations, symbolic ultrametrics, and cographs. J. Math. Biol. 66(1–2), 399–420 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hellmuth M., Wieseke N., Lechner M., Lenhof H.-P., Middendorf M., Stadler P.F.: Phylogenomics with paralogs. PNAS 112(7), 2058–2063 (2015)CrossRefGoogle Scholar
  6. 6.
    Hernandez-Rosales M., Hellmuth M., Wieseke N., Huber K.T., Moulton P.F., Stadler V.: From event-labeled gene trees to species trees. BMC Bioinform. 13(Suppl 19), S6 (2012)Google Scholar
  7. 7.
    Hoàng, C.T.: Perfect graphs. PhD thesis, School of Computer Science, McGill University, Montreal (1985)Google Scholar
  8. 8.
    Jamison B., Olariu S.: P4-reducible-graphs—a class of uniquely tree of uniquely tree-representable graphs. Stud. Appl. Math. 81, 79–87 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Jamison B., Olariu S.: Recognizing P4-sparse graphs in linear time. SIAM J. Comput. 21, 381–406 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Liu, Y., Wang, J., Guo, J., Chen, J.: Cograph editing: complexity and parametrized algorithms. In: Fu, B., Du, D.Z. (eds.) COCOON 2011. Lect. Notes Comp. Sci., vol. 6842, pp. 110–121. Springer, Berlin (2011)Google Scholar
  11. 11.
    Liu, Y., Wang, J., Guo, J., Chen, J.: Complexity and parameterized algorithms for cograph editing. Theor. Comput. Sci. 461(0), 45–54 (2012)Google Scholar
  12. 12.
    Nastos J., Gao Y.: Bounded search tree algorithms for parameterized cograph deletion: efficient branching rules by exploiting structures of special graph classes. Discret. Math. Algorithms Appl. 4, 1250008 (2012)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Sarah J. Berkemer
    • 1
    • 2
  • Ricardo R. C. Chaves
    • 3
  • Adrian Fritz
    • 4
  • Marc Hellmuth
    • 4
    • 5
    Email author
  • Maribel Hernandez-Rosales
    • 3
    • 6
  • Peter F. Stadler
    • 1
    • 2
    • 7
    • 8
    • 9
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Bioinformatics Group, Department of Computer Science, Interdisciplinary Center for BioinformaticsUniversity of LeipzigLeipzigGermany
  3. 3.Departamento de Ciência da Computação (CIC), Instituto de Ciências ExatasUniversidade de BrasíliaBrasíliaBrazil
  4. 4.Center for BioinformaticsSaarland UniversitySaarbrückenGermany
  5. 5.Department of Mathematics and Computer ScienceUniversityof GreifswaldGreifswaldGermany
  6. 6.Instituto de MatemáticasUNAM JuriquillaSantiago de QuerétaroMexico
  7. 7.RNomics GroupFraunhofer Institut für Zelltherapie und ImmunologieLeipzigGermany
  8. 8.Department of Theoretical ChemistryUniversity of ViennaViennaAustria
  9. 9.Santa Fe InstituteSanta FeUSA

Personalised recommendations