### Abstract

One of the simplest heuristics for obtaining a proper coloring of a graph is the First-Fit algorithm: Fix an arbitrary ordering of the vertices and, using the positive integers as the color set, assign to each successive vertex the least integer possible (keeping the coloring proper). This is an example of an on-line algorithm for graph coloring. In the on-line model, a graph is presented one vertex at a time. Each new vertex is given together with all edges joining it to previous vertices. An on-line coloring algorithm assigns a color to each vertex as it is received and once assigned, the color cannot be changed. The performance function, ρ_{ A}(n), of an on-line algorithm A is the maximum over all graphs G on n vertices of the ratio of the number of colors used by A to color G to the chromatic numbers of G. The First-Fit algorithm has performance function n/4. We exhibit an algorithm with sublinear performance function.

Original language | English |
---|---|

Pages (from-to) | 319-325 |

Number of pages | 7 |

Journal | Annals of Discrete Mathematics |

Volume | 43 |

Issue number | C |

DOIs | |

Publication status | Published - 1989 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Annals of Discrete Mathematics*,

*43*(C), 319-325. https://doi.org/10.1016/S0167-5060(08)70584-3

**An On-Line Graph Coloring Algorithm with Sublinear Performance Ratio.** / Lovász, L.; Saks, Michael; Trotter, W. T.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 43, no. C, pp. 319-325. https://doi.org/10.1016/S0167-5060(08)70584-3

}

TY - JOUR

T1 - An On-Line Graph Coloring Algorithm with Sublinear Performance Ratio

AU - Lovász, L.

AU - Saks, Michael

AU - Trotter, W. T.

PY - 1989

Y1 - 1989

N2 - One of the simplest heuristics for obtaining a proper coloring of a graph is the First-Fit algorithm: Fix an arbitrary ordering of the vertices and, using the positive integers as the color set, assign to each successive vertex the least integer possible (keeping the coloring proper). This is an example of an on-line algorithm for graph coloring. In the on-line model, a graph is presented one vertex at a time. Each new vertex is given together with all edges joining it to previous vertices. An on-line coloring algorithm assigns a color to each vertex as it is received and once assigned, the color cannot be changed. The performance function, ρ A(n), of an on-line algorithm A is the maximum over all graphs G on n vertices of the ratio of the number of colors used by A to color G to the chromatic numbers of G. The First-Fit algorithm has performance function n/4. We exhibit an algorithm with sublinear performance function.

AB - One of the simplest heuristics for obtaining a proper coloring of a graph is the First-Fit algorithm: Fix an arbitrary ordering of the vertices and, using the positive integers as the color set, assign to each successive vertex the least integer possible (keeping the coloring proper). This is an example of an on-line algorithm for graph coloring. In the on-line model, a graph is presented one vertex at a time. Each new vertex is given together with all edges joining it to previous vertices. An on-line coloring algorithm assigns a color to each vertex as it is received and once assigned, the color cannot be changed. The performance function, ρ A(n), of an on-line algorithm A is the maximum over all graphs G on n vertices of the ratio of the number of colors used by A to color G to the chromatic numbers of G. The First-Fit algorithm has performance function n/4. We exhibit an algorithm with sublinear performance function.

UR - http://www.scopus.com/inward/record.url?scp=77957773488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957773488&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70584-3

DO - 10.1016/S0167-5060(08)70584-3

M3 - Article

AN - SCOPUS:77957773488

VL - 43

SP - 319

EP - 325

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -