How Tight Is the Bollobás-Komlós Conjecture?

  title={How Tight Is the Bollob{\'a}s-Koml{\'o}s Conjecture?},
  author={Sarmad Abbasi},
  journal={Graphs and Combinatorics},
The bipartite case of the Bollob as and Koml os conjecture states that for every 0; > 0 there is an = ( 0; ) > 0 such that the following statement holds: If G is any graph with (G) n2 + n; then G contains as subgraphs all bipartite graphs, H; satisfying (H) 0 and b(H) n: Here b(H); the bandwidth of H, is the smallest b such that the vertices of H can be ordered as v1; : : : ; vn such that vi H vj implies ji jj b. This conjecture has been proved in [1]. In this note we show that this conjecture… CONTINUE READING

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