### Abstract

A colored graph is a graph whose vertices have been properly, though not necessarily optimally colored, with integers. Colored graphs have a natural orientation in which edges are directed from the end point with smaller color to the end point with larger color. A subgraph of a colored graph is colorful if each of its vertices has a distinct color. We prove that there exists a function f(k, n) such that for any colored graph G, if _{χ}(G)>f(ω(G), n) then G induces either a colorful out directed star with n leaves or a colorful directed path on n vertices. We also show that this result would be false if either alternative was omitted. Our results provide a solution to Problem 115, Discrete Math. 79.

Original language | English (US) |
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Pages (from-to) | 165-169 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 101 |

Issue number | 1-3 |

DOIs | |

State | Published - May 29 1992 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

*Discrete Mathematics*,

*101*(1-3), 165-169. https://doi.org/10.1016/0012-365X(92)90600-K