### 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 |
---|---|

Pages (from-to) | 561-573 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 312 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 6 2012 |

### Fingerprint

### Keywords

- 3-consecutive edge coloring
- Stable cutset
- Stable k-separator
- Strongly independent edge coloring

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

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

**3-consecutive edge coloring of a graph.** / Bujtás, Cs; Sampathkumar, E.; Tuza, Z.; Dominic, Ch; Pushpalatha, L.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 312, no. 3, pp. 561-573. https://doi.org/10.1016/j.disc.2011.04.006

}

TY - JOUR

T1 - 3-consecutive edge coloring of a graph

AU - Bujtás, Cs

AU - Sampathkumar, E.

AU - Tuza, Z.

AU - Dominic, Ch

AU - Pushpalatha, L.

PY - 2012/2/6

Y1 - 2012/2/6

N2 - Three edges e1, e2 and e3 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 e1, e2 and e3 are consecutive edges in G, then e1 or e3 receives the color of e2. 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.

AB - Three edges e1, e2 and e3 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 e1, e2 and e3 are consecutive edges in G, then e1 or e3 receives the color of e2. 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.

KW - 3-consecutive edge coloring

KW - Stable cutset

KW - Stable k-separator

KW - Strongly independent edge coloring

UR - http://www.scopus.com/inward/record.url?scp=81955168110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81955168110&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2011.04.006

DO - 10.1016/j.disc.2011.04.006

M3 - Article

VL - 312

SP - 561

EP - 573

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -