### 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) |
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Title of host publication | Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers |

Pages | 274-286 |

Number of pages | 13 |

DOIs | |

State | Published - Mar 9 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) |
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Volume | 6502 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

City | Konstanz |

Period | 9/21/10 → 9/24/10 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers*(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