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On the graph complement conjecture for minimum rank
2012
Linear Algebra and its Applications
The minimum rank of a graph has been an interesting and well studied parameter investigated by many researchers over the past decade or so. One of the many unresolved questions on this topic is the so-called graph complement conjecture, which grew out of a workshop in 2006. This conjecture asks for an upper bound on the sum of the minimum rank of a graph and the minimum rank of its complement, and may be classified as a Nordhaus-Gaddum type problem involving the graph parameter minimum rank.
doi:10.1016/j.laa.2010.12.024
fatcat:42izy2n34jga3jded7t7dg7pva