We present here 2-approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges de
On cliques and bicliques
β Scribed by Henning, Michael A.
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 97 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
For integers m, n β₯ 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.
π SIMILAR VOLUMES
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
## 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,β1} matrix having one row for each biclique and one column for each vertex of __G__, and such that a pair of 1, β1 entries in a same row cor
A biclique in a graph 1 is a complete bipartite subgraph of 1. We give bounds for the maximum number of edges in a biclique in terms of the eigenvalues of matrix representations of 1. These bounds show a strong similarity with Lova sz's bound (1) for the Shannon capacity of 1. Motivated by this simi
For integers m, n β₯ 2, let f (m, n) be the minimum order of a graph where every vertex belongs to both a clique of cardinality m and an independent set of cardinality n. We show that f (m, n) = ( β m -1 + β n -1) 2 .