The edges of the complete graph on n vertices can be covered by lg n spanning complete bipartite subgraphs. However, the sum of the number of edges in these subgraphs is roughly (n 2 /4)lg n, while a cover consisting of n -1 spanning stars uses only (n -1) 2 edges. We will show that the covering by
On biclique coverings
✍ Scribed by Sergei Bezrukov; Dalibor Fronček; Steven J. Rosenberg; Petr Kovář
- Book ID
- 108113767
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 138 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
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## Abstract A biclique of a graph __G__ is a maximal induced complete bipartite subgraph of __G__. Given a graph __G__, the biclique matrix of __G__ is a {0,1,−1} matrix having one row for each biclique and one column for each vertex of __G__, and such that a pair of 1, −1 entries in a same row cor
For integers m, n ≥ 2, let g(m, n) be the minimum order of a graph, where every vertex belongs to both a clique K m of order m and a biclique K(n, n). or, if m is sufficiently large and (m -1)(n -1) is not an integer.