### Abstract

A subgraph of a plane graph is light if each of its vertices has a small degree in the entire graph. Consider the class script T sign(5) of plane triangulations of minimum degree 5. It is known that each G ∈ script T sign(5) contains a light triangle. From a recent result of Jendrol' and Madaras the existence of light cycles C_{4} and C_{5} in each G ∈ script T sign(5) follows. We prove here that each G ∈ script T sign(5) contains also light cycles C_{6},C_{7},C_{8} and C_{9} such that every vertex is of degree at most 11, 17,29 and 41, respectively. Moreover, we prove that no cycle C_{k} with k≥11 is light in the class script T sign(5).

Original language | English |
---|---|

Pages (from-to) | 453-467 |

Number of pages | 15 |

Journal | Discrete Mathematics |

Volume | 197-198 |

Publication status | Published - Feb 28 1999 |

### Fingerprint

### Keywords

- Cycles
- Light subgraph
- Planar graph
- Triangulation

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics*,

*197-198*, 453-467.