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Packing Bipartite Graphs with Covers of Complete Bipartite Graphs

  • Jérémie Chalopin
  • Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6078)

Abstract

For a set \(\mathcal{S}\) of graphs, a perfect \(\mathcal{S}\)-packing (\(\mathcal{S}\)-factor) of a graph G is a set of mutually vertex-disjoint subgraphs of G that each are isomorphic to a member of \(\mathcal{S}\) and that together contain all vertices of G. If G allows a covering (locally bijective homomorphism) to a graph H, then G is an H-cover. For some fixed H let \(\mathcal{S}(H)\) consist of all H-covers. Let K k,ℓ be the complete bipartite graph with partition classes of size k and ℓ, respectively. For all fixed k,ℓ ≥ 1, we determine the computational complexity of the problem that tests if a given bipartite graph has a perfect \(\mathcal{S}(K_{k,\ell})\)-packing. Our technique is partially based on exploring a close relationship to pseudo-coverings. A pseudo-covering from a graph G to a graph H is a homomorphism from G to H that becomes a covering to H when restricted to a spanning subgraph of G. We settle the computational complexity of the problem that asks if a graph allows a pseudo-covering to K k,ℓ for all fixed k,ℓ ≥ 1.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jérémie Chalopin
    • 1
  • Daniël Paulusma
    • 2
  1. 1.Laboratoire d’Informatique Fondamentale de MarseilleCNRS & Aix-Marseille UniversitéMarseilleFrance
  2. 2.Department of Computer ScienceDurham UniversityDurhamEngland

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