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Graphs and Combinatorics

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

How Tight Is the Bollobás-Komlós Conjecture?

  • Sarmad Abbasi

Abstract.

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.

Keywords

Bipartite Graph Minimum Degree Bipartite Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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