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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Bibliographic Details
Published in:Discrete mathematics Vol. 309; no. 10; pp. 3399 - 3403
Main Authors: Jukna, S., Kulikov, A.S.
Format: Journal Article
Language:English
Published: Elsevier B.V 28.05.2009
Subjects:
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
Online Access:Get full text
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Summary: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