### Abstract

Given a graph G with n vertices and m edges, how many edges must be in the largest chordal subgraph of G? For m=n^{2}/4+1, the answer is 3 n/2-1. For m=n^{2}/3, it is 2 n-3. For m=n^{2}/3+1, it is at least 7 n/3-6 and at most 8 n/3-4. Similar questions are studied, with less complete results, for threshold graphs, interval graphs, and the stars on edges, triangles, and K_{4}'s.

Original language | English |
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Pages (from-to) | 245-253 |

Number of pages | 9 |

Journal | Combinatorica |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1989 |

### Keywords

- AMS subject classification (1980): 05C35

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

Erdös, P., Gyárfás, A., Ordman, E. T., & Zalcstein, Y. (1989). The size of chordal, interval and threshold subgraphs.

*Combinatorica*,*9*(3), 245-253. https://doi.org/10.1007/BF02125893