A colorful cycle in a vertex-colored graph is a graph cycle whose vertices have distinct colors.
If the graph has
colors and the cycle has length , then the cycle contains exactly one vertex of each color.
For vertex-colored graphs, Angles d'Auriac et al. (2016) call a subgraphtropical
if it contains every color, rainbow if it contains
no color more than once, and colorful if it
is both tropical and rainbow. Thus a colorful cycle in a graph with colors is a cycle that is both tropical
and rainbow.
The terminology should not be confused with the use of "rainbow cycle" or "colorful cycle" in edge-colored graph theory, where the colors are
assigned to edges rather than vertices (Alexeev 2005, Ball et al. 2007).
colors and the cycle has length 
, then the cycle contains exactly one vertex of each color.
colors is a cycle that is both tropical
and rainbow.
