… path (cycle) with as few different colors as possible between two given vertices in a colored
graph … approximation algorithms for finding a path with the fewest colors. The complexity of …

… Similarly, Gc is even-pancyclic if it contains properly edge-colored cycles of all possible …
colored cycles and paths for edge-colored graphs. In Section 3 paths and cycles in edge-colored …

… the existence of H-cycles in an H-colored graph, saying nothing … of H-paths and H-cycles of
certain length, in an H-colored graph … known theorems in the theory of properly colored walks. …

… the rainbow path in edge colored graphs. Since lots of results on rainbow paths especially
short rainbow paths are related to … Therefore, we consider long rainbow paths in this section. …

… ℓ ( g ) , such that every graph with girth at least g and with no induced path on ℓ ( g ) vertices
is … k -Coloring problem can be solved in polynomial time for graphs with no induced cycle on …

… consider properly colored cycles in complete graphs and propose … colored complete graph
is properly vertex pancyclic meaning that every vertex is contained in a properly colored cycle …

… color-coding for finding simple paths and cycles of a specified length k, and other small
subgraphs, within a given graph … perfect hash functions, Using the color-coding method we obtain…

… - to the path-problem over a new c-edge-colored graph. Given … s−t path P in Gc , we construct
a new non-colored graph G by … It is easy to see that G will contains a s−t path, cycles and …

… in (randomly) colored random graphs. Our basic interest will be in what we call zebraic
paths and cycles. We assume that the edges of a graph G have been colored black or white. A …

… for paths. In particular, for a connected graph G, they defined the proper connection number
as the minimum number of colors that one needs so that there is a properly colored path …