𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On cliques and bicliques

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Approximating Clique and Biclique Proble
✍ Dorit S. Hochbaum πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 317 KB

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

Covering cliques with spanning bicliques
✍ KοΏ½ndgen, AndrοΏ½ πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 192 KB

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

Biclique graphs and biclique matrices
✍ Marina Groshaus; Jayme L. Szwarcfiter πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 203 KB

## 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,βˆ’1} matrix having one row for each biclique and one column for each vertex of __G__, and such that a pair of 1, βˆ’1 entries in a same row cor

Bicliques and Eigenvalues
✍ Willem H. Haemers πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 147 KB

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

A note on cliques and independent sets
✍ Entringer, Roger C.; Goddard, Wayne; Henning, Michael A. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 58 KB πŸ‘ 2 views

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) = ( √ m -1 + √ n -1) 2 .