Inducing regulation of any digraphs

  • Authors:

  • Joanna Górska;Zdzisław Skupień

  • Affiliations:

  • Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland;Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

For a given structure D (digraph, multidigraph, or pseudodigraph) and an integer r large enough, a smallest inducing r-regularization of D is constructed. This regularization is an r-regular superstructure of the smallest possible order with bounded arc multiplicity, and containing D as an induced substructure. The sharp upper bound on the number, @r, of necessary new vertices among such superstructures for n-vertex general digraphs D is determined, @r being called the inducing regulation number of D. For @D@?(D) being the maximum among semi-degrees in D, simple n-vertex digraphs D with largest possible @r are characterized if either r=@D@?(D) or r=@D@?(D) (where the case r=@D@? is not a trivial subcase of r=@D@?).