### Abstract

In this paper, we introduce a variant of graph coloring which is motivated by the channel assignment problem. In this variant, called no-hole 2-distant coloring, we seek to color the vertices of a graph with positive integers so that two adjacent vertices get integers which differ by more than 1 (the 2-distant requirement) and so that the set of integers used as colors is a consecutive set (the no-hole requirement). We study the question of what graphs have such colorings. We also study the question of what graphs have such colorings which are near-optimal in the sense that the span, or separation between the largest and smallest colors used, is no more than one larger than the minimum span in a non-adjacent coloring which may have holes.

Original language | English (US) |
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Pages (from-to) | 139-144 |

Number of pages | 6 |

Journal | Mathematical and Computer Modelling |

Volume | 17 |

Issue number | 11 |

DOIs | |

State | Published - Jun 1993 |

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Computer Science Applications

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## Cite this

*Mathematical and Computer Modelling*,

*17*(11), 139-144. https://doi.org/10.1016/0895-7177(93)90265-Z