TY - JOUR
T1 - On biclique coverings
AU - Bezrukov, Sergei
AU - Fronček, Dalibor
AU - Rosenberg, Steven J.
AU - Kovář, Petr
PY - 2008/2/6
Y1 - 2008/2/6
N2 - It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bipartite graph Kn, n with a perfect matching removed can be covered by k bicliques, then n ≤ fenced(frac(k, ⌊ frac(k, 2) ⌋)). We give a slightly simplified proof and we show that the result is tight. Moreover, we use the result to prove analogous bounds for coverings of some other classes of graphs by bicliques.
AB - It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bipartite graph Kn, n with a perfect matching removed can be covered by k bicliques, then n ≤ fenced(frac(k, ⌊ frac(k, 2) ⌋)). We give a slightly simplified proof and we show that the result is tight. Moreover, we use the result to prove analogous bounds for coverings of some other classes of graphs by bicliques.
KW - Bicliques
KW - Graph composition
KW - Graph coverings
KW - Lexicographic product
KW - Sperner's Theorem
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U2 - 10.1016/j.disc.2006.11.045
DO - 10.1016/j.disc.2006.11.045
M3 - Article
AN - SCOPUS:36248977676
SN - 0012-365X
VL - 308
SP - 319
EP - 323
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 2-3
ER -