### Abstract

We study the maximum differential graph coloring problem, in which the goal is to find a vertex labeling for a given undirected graph that maximizes the label difference along the edges. This problem has its origin in map coloring, where not all countries are necessarily contiguous. We define the differential chromatic number and establish the equivalence of the maximum differential coloring problem to that of k-Hamiltonian path. As computing the maximum differential coloring is NP-Complete, we describe an exact backtracking algorithm and a spectral-based heuristic. We also discuss lower bounds and upper bounds for the differential chromatic number for several classes of graphs.

Original language | English (US) |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 274-286 |

Number of pages | 13 |

Volume | 6502 LNCS |

DOIs | |

State | Published - 2011 |

Event | 18th International Symposium on Graph Drawing, GD 2010 - Konstanz, Germany Duration: Sep 21 2010 → Sep 24 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 6502 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 18th International Symposium on Graph Drawing, GD 2010 |
---|---|

Country | Germany |

City | Konstanz |

Period | 9/21/10 → 9/24/10 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 6502 LNCS, pp. 274-286). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS). https://doi.org/10.1007/978-3-642-18469-7_25

**On maximum differential graph coloring.** / Hu, Yifan; Kobourov, Stephen G; Veeramoni, Sankar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 6502 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6502 LNCS, pp. 274-286, 18th International Symposium on Graph Drawing, GD 2010, Konstanz, Germany, 9/21/10. https://doi.org/10.1007/978-3-642-18469-7_25

}

TY - GEN

T1 - On maximum differential graph coloring

AU - Hu, Yifan

AU - Kobourov, Stephen G

AU - Veeramoni, Sankar

PY - 2011

Y1 - 2011

N2 - We study the maximum differential graph coloring problem, in which the goal is to find a vertex labeling for a given undirected graph that maximizes the label difference along the edges. This problem has its origin in map coloring, where not all countries are necessarily contiguous. We define the differential chromatic number and establish the equivalence of the maximum differential coloring problem to that of k-Hamiltonian path. As computing the maximum differential coloring is NP-Complete, we describe an exact backtracking algorithm and a spectral-based heuristic. We also discuss lower bounds and upper bounds for the differential chromatic number for several classes of graphs.

AB - We study the maximum differential graph coloring problem, in which the goal is to find a vertex labeling for a given undirected graph that maximizes the label difference along the edges. This problem has its origin in map coloring, where not all countries are necessarily contiguous. We define the differential chromatic number and establish the equivalence of the maximum differential coloring problem to that of k-Hamiltonian path. As computing the maximum differential coloring is NP-Complete, we describe an exact backtracking algorithm and a spectral-based heuristic. We also discuss lower bounds and upper bounds for the differential chromatic number for several classes of graphs.

UR - http://www.scopus.com/inward/record.url?scp=79952264539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952264539&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-18469-7_25

DO - 10.1007/978-3-642-18469-7_25

M3 - Conference contribution

AN - SCOPUS:79952264539

SN - 9783642184680

VL - 6502 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 274

EP - 286

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -