Subgraphs of Randomk-Edge-Colouredk-Regular Graphs
2009 ◽
Vol 18
(4)
◽
pp. 533-549
◽
Keyword(s):
LetG=G(n) be a randomly chosenk-edge-colouredk-regular graph with 2nvertices, wherek=k(n). Such a graph can be obtained from a random set ofkedge-disjoint perfect matchings ofK2n. Leth=h(n) be a graph withm=m(n) edges such thatm2+mk=o(n). Using a switching argument, we find an asymptotic estimate of the expected number of subgraphs ofGisomorphic toh. Isomorphisms may or may not respect the edge colouring, and other generalizations are also presented. Special attention is paid to matchings and cycles.The results in this paper are essential to a forthcoming paper of McLeod in which an asymptotic estimate for the number ofk-edge-colouredk-regular graphs fork=o(n5/6) is found.
2000 ◽
Vol 9
(3)
◽
pp. 241-263
◽
2017 ◽
Vol 11
(1)
◽
pp. 11-38
Keyword(s):
Keyword(s):
1966 ◽
Vol 18
◽
pp. 1091-1094
◽