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Packing Hamilton Cycles Online

Part of: Graph theory

Published online by Cambridge University Press:  22 March 2018

JOSEPH BRIGGS ,
ALAN FRIEZE ,
MICHAEL KRIVELEVICH ,
PO-SHEN LOH  and
BENNY SUDAKOV
JOSEPH BRIGGS
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: jbriggs@andrew.cmu.edu, alan@random.math.cmu.edu, ploh@cmu.edu)
ALAN FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: jbriggs@andrew.cmu.edu, alan@random.math.cmu.edu, ploh@cmu.edu)
MICHAEL KRIVELEVICH
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel (e-mail: krivelev@post.tau.ac.il)
PO-SHEN LOH
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: jbriggs@andrew.cmu.edu, alan@random.math.cmu.edu, ploh@cmu.edu)
BENNY SUDAKOV
Affiliation:
Department of Mathematics, ETH, 8092 Zurich, Switzerland (e-mail: benjamin.sudakov@math.ethz.ch)
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Abstract

It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge-disjoint Hamilton cycles [4, 9, 13]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ⩾ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to colour the edges online with σ colours so that at time τ2σ each colour class is Hamiltonian.

MSC classification

Primary: 05C80: Random graphs
Secondary: 05C15: Coloring of graphs and hypergraphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Special Issue 4: Special Issue: Oberwolfach Workshop , July 2018 , pp. 475 - 495
Copyright
Copyright © Cambridge University Press 2018 

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References

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