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An Improved Upper Bound on the Density of Universal Random Graphs

  • Domingos DellamonicaJr.
  • Yoshiharu Kohayakawa
  • Vojtěch Rödl
  • Andrzej Ruciński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7256)

Abstract

We give a polynomial time randomized algorithm that, on receiving as input a pair (H,G) of n-vertex graphs, searches for an embedding of H into G. If H has bounded maximum degree and G is suitably dense and pseudorandom, then the algorithm succeeds with high probability. Our algorithm proves that, for every integer d ≥ 3 and suitable constant C = C d , as n → ∞, asymptotically almost all graphs with n vertices and \(\lfloor Cn^{2-1/d}\log^{1/d}n\rfloor\) edges contain as subgraphs all graphs with n vertices and maximum degree at most d.

Keywords

Bipartite Graph Perfect Match Random Graph Auxiliary Graph Vertex Class 
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 Berlin Heidelberg 2012

Authors and Affiliations

  • Domingos DellamonicaJr.
    • 1
  • Yoshiharu Kohayakawa
    • 1
    • 2
  • Vojtěch Rödl
    • 1
  • Andrzej Ruciński
    • 1
    • 3
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  3. 3.Department of Discrete MathematicsAdam Mickiewicz UniversityPoznańPoland

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