### Abstract

We show the following. (1) For each integer n≥12, there exists a uniquely 3-colorable graph with n vertices and without any triangles. (2) There exist infinitely many uniquely 3-colorable regular graphs without any triangles. It follows that there exist infinitely many uniquely k-colorable regular graphs having no subgraph isomorphic to the complete graph K_{k} with k vertices for any integer k≥3.

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

Pages (from-to) | 21-27 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 112 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 25 1993 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*112*(1-3), 21-27. https://doi.org/10.1016/0012-365X(93)90220-N

}

*Discrete Mathematics*, vol. 112, no. 1-3, pp. 21-27. https://doi.org/10.1016/0012-365X(93)90220-N

**On uniquely 3-colorable graphs.** / Chao, Chong Yun; Chen, Zhibo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On uniquely 3-colorable graphs

AU - Chao, Chong Yun

AU - Chen, Zhibo

PY - 1993/3/25

Y1 - 1993/3/25

N2 - We show the following. (1) For each integer n≥12, there exists a uniquely 3-colorable graph with n vertices and without any triangles. (2) There exist infinitely many uniquely 3-colorable regular graphs without any triangles. It follows that there exist infinitely many uniquely k-colorable regular graphs having no subgraph isomorphic to the complete graph Kk with k vertices for any integer k≥3.

AB - We show the following. (1) For each integer n≥12, there exists a uniquely 3-colorable graph with n vertices and without any triangles. (2) There exist infinitely many uniquely 3-colorable regular graphs without any triangles. It follows that there exist infinitely many uniquely k-colorable regular graphs having no subgraph isomorphic to the complete graph Kk with k vertices for any integer k≥3.

UR - http://www.scopus.com/inward/record.url?scp=38249002114&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249002114&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(93)90220-N

DO - 10.1016/0012-365X(93)90220-N

M3 - Article

AN - SCOPUS:38249002114

VL - 112

SP - 21

EP - 27

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -