On cliques and bicliques

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


For integers m, n ≥ 2, let g(m, n) be the minimum order of a graph, where every vertex belongs to both a clique Km of order m and a biclique K(n, n). We show that g(m, n) = 2(m + n - 2) if m ≤ n-2. Furthermore, for m ≥ n - 1, we establish that g(m, n) = [(√m - 1 + √n - 1)2] if [√(m - 1)(n - 1)] ≡ 0 mod(n - 1) or, if m is sufficiently large and √(m - 1)(n - 1) is not an integer.

Original languageEnglish
Pages (from-to)60-66
Number of pages7
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - May 2000
Externally publishedYes


  • Bicliques
  • Cliques
  • Homogeneous embeddings

ASJC Scopus subject areas

  • Geometry and Topology


Dive into the research topics of 'On cliques and bicliques'. Together they form a unique fingerprint.

Cite this