Oriented star packings

  • Authors:

  • Richard C. Brewster;Pavol Hell;Romeo Rizzi

  • Affiliations:

  • Department of Mathematics and Statistics, Thompson Rivers University, PO BOX 3010, 900 McGill Road, Kamloops, BC, Canada, V2C 5N3;School of Computer Science, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6;Università degli Studi di Udine, Facoltà di Ingegneria -- Dipartimento di Matematica e Informatica, Via delle Scienze, 208, I-33100 Udine, Italy

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2008

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Abstract

Given a (possibly infinite) family S of oriented stars, an S-packing in a digraph D is a collection of vertex disjoint subgraphs of D, each isomorphic to a member of S. The S-Packing problem asks for the maximum number of vertices, of a host digraph D, that can be covered by an S-packing of D. We prove a dichotomy for the decision version of the S-packing problem, giving an exact classification of which problems are polynomial time solvable and which are NP-complete. For the polynomial problems, we provide Hall type min-max theorems, including versions for (locally) degree-constrained variants of the problems. An oriented star can be specified by a pair of (k,@?)@?N^2@?(0,0) denoting the number of out- and in-neighbours of the centre vertex. For p,q,d@?N@?{~}, we denote by S"p","q","d the family of stars (k,@?) such that k=