On optimal exact coverings of a graph in the class of weakly dense bases
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| 024 | 7 | 0 | |a 10.1515/1569392041938776 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/1569392041938776 | ||
| 100 | 1 | |a Lozhkina |D Z. S. | |
| 245 | 1 | 0 | |a On optimal exact coverings of a graph in the class of weakly dense bases |h [Elektronische Daten] |c [Z. S. Lozhkina] |
| 520 | 3 | |a We consider the problem on covering a non-oriented connected graph without loops and multiple edges by graphs of arbitrary finite bases. We introduce the notions of complexity of a covering, complexity of a graph and the Shannon function. In accordance with the asymptotic behaviour of the Shannon function, we introduce two classes of bases, almost dense and weakly dense bases. For the class of weakly dense bases and a special subclass of this class we suggest methods of constructing optimal exact coverings of a graph by bipartite basic graphs and find estimates of the complexity of such coverings. The suggested methods are based on algorithms for optimal exact covering of (0, 1)-matrices by arbitrary (0, 1)-matrices and on the connection between coverings of (0, 1)-matrices and coverings of a graph by bipartite graphs. | |
| 540 | |a Copyright 2004, Walter de Gruyter | ||
| 773 | 0 | |t Discrete Mathematics and Applications |d Walter de Gruyter |g 14/4(2004-08-01), 385-407 |x 0924-9265 |q 14:4<385 |1 2004 |2 14 |o dma | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/1569392041938776 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/1569392041938776 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Lozhkina |D Z. S. | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Discrete Mathematics and Applications |d Walter de Gruyter |g 14/4(2004-08-01), 385-407 |x 0924-9265 |q 14:4<385 |1 2004 |2 14 |o dma | ||
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| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||