A split graph counterexample disproves the biclique partition conjecture for split graphs, with an infinite family of examples and a solution to the singular n-tournament binary rank problem.
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f(n,k) satisfies (1+o(1)) c1(k) n^{1/(⌈k/2⌉+1)} ≤ f(n,k) ≤ (1+o(1)) c2(k) n^{1/(⌊k/2⌋+1)+o(1)} for fixed k≥2.
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A counterexample to the conjecture on Biclique Partition number of Split Graphs and related problems
A split graph counterexample disproves the biclique partition conjecture for split graphs, with an infinite family of examples and a solution to the singular n-tournament binary rank problem.
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Almost balanced ordered biclique covering of graphs
f(n,k) satisfies (1+o(1)) c1(k) n^{1/(⌈k/2⌉+1)} ≤ f(n,k) ≤ (1+o(1)) c2(k) n^{1/(⌊k/2⌋+1)+o(1)} for fixed k≥2.