### 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 - Jan 1 1993 |

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### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Computer Science Applications

### Cite this

*Mathematical and Computer Modelling*,

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

}

*Mathematical and Computer Modelling*, vol. 17, no. 11, pp. 139-144. https://doi.org/10.1016/0895-7177(93)90265-Z

**No-hole 2-distant colorings.** / Roberts, Fred.

Research output: Contribution to journal › Article

TY - JOUR

T1 - No-hole 2-distant colorings

AU - Roberts, Fred

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041597722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041597722&partnerID=8YFLogxK

U2 - 10.1016/0895-7177(93)90265-Z

DO - 10.1016/0895-7177(93)90265-Z

M3 - Article

AN - SCOPUS:0041597722

VL - 17

SP - 139

EP - 144

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 11

ER -