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Almost Every Tree With m Edges Decomposes K2m,2m

Published online by Cambridge University Press:  03 December 2013

M. DRMOTA  and
A. LLADÓ
M. DRMOTA
Affiliation:
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Vienna, Austria (e-mail: michael.drmota@tuwien.ac.at
A. LLADÓ
Affiliation:
Departament de Matemàtica Aplicada~IV, Universitat Politècnica de Catalunya–BarcelonaTech, Barcelona, Spain (e-mail: allado@ma4.upc.edu)
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Abstract

We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost surely a tree with m edges decomposes the complete graph with O(m2) edges. An ingredient of the proof consists in showing that the bipartition classes of the base tree of a random tree have roughly equal size.

Keywords

Primary 05C51Secondary 05C80

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 1 , January 2014 , pp. 50 - 65
Copyright
Copyright © Cambridge University Press 2013 

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