Geodesic
Multicoloured Hamilton cycles in random graphs; an anti-Ramsey threshold
The electronic journal of combinatorics, Tome 2 (1995)
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Let the edges of a graph $G$ be coloured so that no colour is used more than $k$ times. We refer to this as a $k$-bounded colouring. We say that a subset of the edges of $G$ is multicoloured if each edge is of a different colour. We say that the colouring is $\cal H$-good, if a multicoloured Hamilton cycle exists i.e., one with a multicoloured edge-set. Let ${\cal AR}_k$ = $\{G :$ every $k$-bounded colouring of $G$ is $\cal H$-good$\}$. We establish the threshold for the random graph $G_{n,m}$ to be in ${\cal AR}_k$.
DOI : 10.37236/1213
Classification : 05C80, 05C15, 05C45, 05C38
Mots-clés : anti-Ramsey threshold, colour, colouring, multicoloured Hamilton cycle, threshold, random graph 
@article{10_37236_1213,
     author = {Colin Cooper and Alan Frieze},
     title = {Multicoloured {Hamilton} cycles in random graphs; an {anti-Ramsey} threshold},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1213},
     zbl = {0827.05055},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1213/}
}
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Colin Cooper; Alan Frieze. Multicoloured Hamilton cycles in random graphs; an anti-Ramsey threshold. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1213

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