On covering graphs by complete bipartite subgraphs

We prove that, if a graph with e edges contains m vertex-disjoint edges, then m 2 / e complete bipartite subgraphs are necessary to cover all its edges. Similar lower bounds are also proved for fractional covers. For sparse graphs, this improves the well-known fooling set lower bound in communicatio...

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Vydané v:Discrete mathematics Ročník 309; číslo 10; s. 3399 - 3403
Hlavní autori: Jukna, S., Kulikov, A.S.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 28.05.2009
Predmet:
Biclique
Boolean functions
Communication complexity
Edge clique covering number
Fractional covers
Boolean functions
Communication complexity
Edge clique covering number
Fractional covers
Biclique
ISSN:0012-365X, 1872-681X
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Popis
Shrnutí:We prove that, if a graph with e edges contains m vertex-disjoint edges, then m 2 / e complete bipartite subgraphs are necessary to cover all its edges. Similar lower bounds are also proved for fractional covers. For sparse graphs, this improves the well-known fooling set lower bound in communication complexity. We also formulate several open problems about covering problems for graphs whose solution would have important consequences in the complexity theory of boolean functions.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2008.09.036