  Given an $n$ vertex graph whose edges have colored from one of $r$ colors
$C=\{c_1,c_2,\ldots,c_r\}$, we define the Hamilton cycle color profile $hcp(G)$
to be the set of vectors $(m_1,m_2,\ldots,m_r)\in [0,n]^r$ such that there
exists a Hamilton cycle that is the concatenation of $r$ paths
$P_1,P_2,\ldots,P_r$, where $P_i$ contains $m_i$ edges. We study $hcp(G_{n,p})$
when the edges are randomly colored. We discuss the profile close to the
threshold for the existence of a Hamilton cycle and the threshold for when
$hcp(G_{n,p})=\{(m_1,m_2,\ldots,m_r)\in [0,n]^r:m_1+m_2+\cdots+m_r=n\}$.
