### Abstract

Three edges e_{1}, e_{2} and e_{3} in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The 3-consecutive edge coloring number ψ′_{3c}(G) of G is the maximum number of colors permitted in a coloring of the edges of G such that if e_{1}, e_{2} and e_{3} are consecutive edges in G, then e_{1} or e^{3} receives the color of e^{2}. Here we initiate the study of ψ′_{3c}(G). A close relation between 3-consecutive edge colorings and a certain kind of vertex cut is pointed out, and general bounds on ψ′_{3c} are given in terms of other graph invariants. Algorithmically, the distinction between ψ′ _{3c}=1 and ψ′_{3c}=2 is proved to be intractable, while efficient algorithms are designed for some particular graph classes.

Original language | English |
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Pages (from-to) | 561-573 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 312 |

Issue number | 3 |

DOIs | |

Publication status | Published - febr. 6 2012 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

*Discrete Mathematics*,

*312*(3), 561-573. https://doi.org/10.1016/j.disc.2011.04.006