On a conjecture of Graham and Häggkvist for random trees

  • Michael Drmota
  • Anna Lladó
Conference paper
Part of the CRM Series book series (PSNS, volume 16)


A conjecture of Graham and Häggkvist says that every tree with m edges decomposes the complete bipartite graph K m,m . By establishing some properties of random trees with the use of singularity analysis of generating functions, we prove that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K 2m,2m .


Discrete Math Cayley Graph Base Tree Random Tree Complete Bipartite Graph 
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Copyright information

© Scuola Normale Superiore Pisa 2013

Authors and Affiliations

  • Michael Drmota
    • 1
  • Anna Lladó
    • 2
  1. 1.Institute of Discrete Mathematics and GeometryVienna University of TechnologyViennaAustria
  2. 2.Dept. Matemàtica Aplicada 4Universitat Politècnica de Catalunya-BarcelonaTechBarcelonaSpain

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