Relations between graphs

Authors

  • Jan Hubička Charles University, Czech Republic
  • Jürgen Jost Max Planck Institute for Mathematics in the Sciences, Germany and University of Leipzig, Germany and Santa Fe Institute, United States
  • Yangjing Long Max Planck Institute for Mathematics in the Sciences, Germany
  • Peter F. Stadler University of Leipzig, Germany and Max Planck Institute for Mathematics in the Sciences, Germany and Santa Fe Institute, United States and Fraunhofer-Institut für Zelltherapie und Immunologie IZI, Germany and University of Vienna, Austria and University of Copenhagen, Denmark
  • Ling Yang Fudan University, China

DOI:

https://doi.org/10.26493/1855-3974.335.d57

Keywords:

Generalized surjective graph homomorphism, R-reduced graph, R-retraction, binary relation, multihomomorphism, R-core, cocore

Abstract

Given two graphs G = (VG, EG) and H = (VH, EH), we ask under which conditions there is a relation R ⊆ VG × VH that generates the edges of H given the structure of the graph G. This construction can be seen as a form of multihomomorphism. It generalizes surjective homomorphisms of graphs and naturally leads to notions of R-retractions, R-cores, and R-cocores of graphs. Both R-cores and R-cocores of graphs are unique up to isomorphism and can be computed in polynomial time.

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Published

2012-12-24

Issue

Vol. 6 No. 2 (2013)

Section

Articles

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/