Graphs and Combinatorics

, Volume 16, Issue 2, pp 129–137 | Cite as

How Tight Is the Bollobás-Komlós Conjecture?

  • Sarmad Abbasi


The bipartite case of the Bollobás and Komlós conjecture states that for every Δ0, γ>0 there is an α=α(Δ0, γ) >0 such that the following statement holds: If G is any graph with minimum degree at least \(\) then G contains as subgraphs all n vertex bipartite graphs, H, satisfying¶
¶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 viHvj implies |ij|≤b.¶ This conjecture has been proved in [1]. Answering a question of E. Szemerédi [6] we show that this conjecture is tight in the sense that as γ→0 then α→0. More precisely, we show that for any \(\) there is a Δ0 such that that α(Δ0, γ)≤4 γ.


Bipartite Graph Minimum Degree Bipartite Case 


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Copyright information

© Springer-Verlag Tokyo 2000

Authors and Affiliations

  • Sarmad Abbasi
    • 1
  1. 1.Department of Computer Science, Quaid-i-Azam University, Islamabad 45320, PakistanPK

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