TY - JOUR
T1 - Packing Hamilton Cycles Online
AU - Briggs, Joseph
AU - Frieze, Alan
AU - Krivelevich, Michael
AU - Loh, Po Shen
AU - Sudakov, Benny
N1 - Publisher Copyright:
© 2018 Cambridge University Press.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85044203474&partnerID=8YFLogxK
U2 - 10.1017/S0963548318000159
DO - 10.1017/S0963548318000159
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AN - SCOPUS:85044203474
SN - 0963-5483
VL - 27
SP - 475
EP - 495
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 4
ER -