Chalopin, J. and Paulusma, Daniel (2010) 'Packing bipartite graphs with covers of complete bipartite graphs.', in Algorithms and complexity, 7th International Conference, CIAC 2010, 26-28 May 2010, Rome, Italy ; proceedings. Berlin ; Heidelberg: Springer, 276-287 . Lecture notes in computer science. (6078).
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.
|Item Type:||Book chapter|
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|Publisher Web site:||http://dx.doi.org/10.1007/978-3-642-13073-1_25|
|Record Created:||07 Oct 2010 12:05|
|Last Modified:||03 Apr 2013 13:20|
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