Paths and cycles in colored graphs

@article{Broersma2001PathsAC,
  title={Paths and cycles in colored graphs},
  author={Hajo Broersma and Xueliang Li and Gerhard J. Woeginger and Shenggui Zhang},
  journal={Australasian J. Combinatorics},
  year={2001},
  volume={31},
  pages={299-312}
}
Let G be an (edge-)colored graph. A path (cycle) is called monochromatic if all of its edges have the same color, and is called heterochromatic if all of its edges have different colors. In this paper, some sufficient conditions for the existence of (long) monochromatic paths and cycles, and those for the existences of long heterochromatic paths and cycles are obtained. It is proved that the problem of finding a path (cycle) with as few different colors as possible in a colored graph is NP-hard… CONTINUE READING