@inbook{4f75bdbf648347e191bbf2349c0ffe25,

title = "On Hamilton Cycles in 3-Connected Cubic Maps",

abstract = "We show that the probability of a 3-connected cubic map with 2n vertices being hamiltonian tends to zero exponentially with with n. We show that if there is one 3-connected triangulation which is not 4-colourable then the probability that a 3-connected triangulation is 4-colourable tends to zero exponentially with n. These results both follow easily from the result proved here that any given 3-connected triangulation, T, is contained (with the boundary of T an interior 3-cycle) in a 3-connected triangulation with 2n faces with probability 1 + 0(cn), c < 1.",

author = "Richmond, {L. Bruce} and Robinson, {R. W.} and Wormald, {N. C.}",

year = "1985",

month = jan,

day = "1",

doi = "10.1016/S0304-0208(08)73003-2",

language = "English",

isbn = "9780444878038",

volume = "115",

series = "North-Holland Mathematics Studies",

pages = "141--149",

editor = "B.R. Alspach and C.D. Godsil",

booktitle = "Annals of Discrete Mathematics (27)",

edition = "C",

}