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Conference Papers Year : 2016

On Maximal Chain Subgraphs and Covers of Bipartite Graphs


In this paper, we address three related problems. One is the enumeration of all the maximal edge induced chain subgraphs of a bipartite graph, for which we provide a polynomial delay algorithm. We give bounds on the number of maximal chain subgraphs for a bipartite graph and use them to establish the input-sensitive complexity of the enumeration problem. The second problem we treat is the one of finding the minimum number of chain subgraphs needed to cover all the edges a bipartite graph. For this we provide an exact exponential algorithm with a non trivial complexity. Finally, we approach the problem of enumerating all minimal chain subgraph covers of a bipartite graph and show that it can be solved in quasi-polynomial time.
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hal-01388546 , version 1 (30-05-2017)



Tiziana Calamoneri, Mattia Gastaldello, Arnaud Mary, Marie-France Sagot, Blerina Sinaimeri. On Maximal Chain Subgraphs and Covers of Bipartite Graphs. Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Aug 2016, Helsinki, Finland. pp.137-150, ⟨10.1007/978-3-319-44543-4_11⟩. ⟨hal-01388546⟩
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