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On Minrank and Forbidden Subgraphs
2018
International Workshop on Approximation Algorithms for Combinatorial Optimization
The minrank over a field F of a graph G on the vertex set {1, 2, . . . , n} is the minimum possible rank of a matrix M ∈ F n×n such that M i,i = 0 for every i, and M i,j = 0 for every distinct nonadjacent vertices i and j in G. For an integer n, a graph H, and a field F, let g(n, H, F) denote the maximum possible minrank over F of an n-vertex graph whose complement contains no copy of H. In this paper we study this quantity for various graphs H and fields F. For finite fields, we prove by a
doi:10.4230/lipics.approx-random.2018.42
dblp:conf/approx/Haviv18a
fatcat:d732lo7pjfdqjofh7iu2aijlri