Switch-Based Markov Chains for Sampling Hamiltonian Cycles in Dense Graphs
Keyword(s):
We consider the irreducibility of switch-based Markov chains for the approximate uniform sampling of Hamiltonian cycles in a given undirected dense graph on $n$ vertices. As our main result, we show that every pair of Hamiltonian cycles in a graph with minimum degree at least $n/2+7$ can be transformed into each other by switch operations of size at most 10, implying that the switch Markov chain using switches of size at most 10 is irreducible. As a proof of concept, we also show that this Markov chain is rapidly mixing on dense monotone graphs.
2011 ◽
Vol 48
(04)
◽
pp. 901-910
◽
Keyword(s):
Keyword(s):
2011 ◽
Vol 48
(4)
◽
pp. 901-910
◽
Keyword(s):
1990 ◽
Vol 27
(03)
◽
pp. 545-556
◽
Keyword(s):
2004 ◽
Vol 2004
(8)
◽
pp. 421-429
◽
Keyword(s):
1984 ◽
Vol 25
(4)
◽
pp. 463-472
1998 ◽
Vol 93
(443)
◽
pp. 1055-1067
◽
Keyword(s):