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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| Published in: | Discrete mathematics Vol. 309; no. 10; pp. 3399 - 3403 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
28.05.2009
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| ISSN: | 0012-365X, 1872-681X |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Jukna, S. Kulikov, A.S. |
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| Cites_doi | 10.1007/s003730050068 10.1017/S0963548397003064 10.1017/S0963548306007620 10.1007/s00224-002-1068-0 10.1016/S0012-365X(03)00227-9 10.1007/BF02579381 10.1016/0012-365X(75)90058-8 10.1007/BF02579163 10.1007/BF02122698 10.1002/j.1538-7305.1971.tb02618.x 10.1137/S0895480192238482 10.1016/0012-365X(80)90109-0 10.1137/S0097539794261556 10.1109/SFCS.1986.15 10.1007/BF01747074 |
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| Keywords | Boolean functions Communication complexity Edge clique covering number Fractional covers Biclique |
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| Snippet | 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.... |
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| SubjectTerms | Biclique Boolean functions Communication complexity Edge clique covering number Fractional covers |
| Title | On covering graphs by complete bipartite subgraphs |
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