Packing bipartite graphs with covers of complete bipartite graphs

Chalopin, J.; Paulusma, D.

Abstract

For a set of graphs, a perfect -packing (-factor) of a graph G is a set of mutually vertex-disjoint subgraphs of G that each are isomorphic to a member of 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 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 -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.

Citation

Chalopin, J., & Paulusma, D. (2010, December). Packing bipartite graphs with covers of complete bipartite graphs. Presented at 7th International Conference on Algorithms and Complexity, Rome, Italy

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 7th International Conference on Algorithms and Complexity
• Publication Date: Jan 1, 2010
• Deposit Date: Oct 6, 2010
• Print ISSN: 0302-9743
• Publisher: Springer Verlag
• Pages: 276-287
• Series Title: Lecture notes in computer science
• Series Number: 6078
• Edition: 7th
• Book Title: Algorithms and complexity, 7th International Conference, CIAC 2010, 26-28 May 2010, Rome, Italy ; proceedings.
• DOI: https://doi.org/10.1007/978-3-642-13073-1_25
• Public URL: https://durham-repository.worktribe.com/output/1159326