On the Number of Maximal Bipartite Subgraphs of a Graph
We show new lower and upper bounds on the number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105^{n/10} ~= 1.5926^n such subgraphs, which improves an earlier lower bound by Schiermeyer (1996). We show an upper bound of n . 12^{n/4} ~= n . 1.8613^n and give an algorithm that lists all maximal induced bipartite subgraphs in time proportional to this bound. This is used in an algorithm for checking 4-colourability of a graph running within the same time bound.
2000 ◽
Vol 32
(01)
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pp. 244-255
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2005 ◽
Vol 70
(10)
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pp. 1193-1197
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2007 ◽
Vol 03
(04)
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pp. 503-511
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2012 ◽
Vol 08
(06)
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pp. 1367-1386
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2000 ◽
Vol 32
(1)
◽
pp. 244-255
◽
Keyword(s):