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The minimum biclique edge cover problem (MBECP) is NP-hard for general graphs. It is known that if we restrict an input graph to the bipartite domino-free class, MBECP can be solved within polynomial-time of input graph size. We show a new polynomial-time solvable graph class for MBECP that is characterized by three forbidden graphs, a domino, a gem and K4. This graph class allows that an input graph is non-bipartite, and includes the bipartite domino-free graph class properly.
Anish Man Singh SHRESTHA Asahi TAKAOKA Satoshi TAYU Shuichi UENO
The logic mapping problem and the problem of finding a largest sub-crossbar with no defects in a nano-crossbar with nonprogrammable-crosspoint defects and disconnected-wire defects are known to be NP-hard. This paper shows that for nano-crossbars with only disconnected-wire defects, the former remains NP-hard, while the latter can be solved in polynomial time.
For a graph G, a biclique edge partition SBP(G) is a collection of bicliques (complete bipartite subgraphs) Bi such that each edge of G is contained in exactly one Bi. The Minimum Biclique Edge Partition Problem (MBEPP) asks for SBP(G) with the minimum size. In this paper, we show that for arbitrary small ε>0, (6053/6052-ε)-approximation of MBEPP is NP-hard.