## Abstract

We first present new structural properties of a two-pair in various graphs. A two-pair is used in a well-known characterization of weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K_{2, 3}, over(4 P_{2}, -), over(P_{2} ∪ P_{4}, -), over(P_{6}, -), H_{1}, H_{2}, H_{3})-free graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the so called [4, 4, 2] graphs. The proof of the theorem constructively finds the representation. Thus, we obtain an algorithm to construct an edge intersection model of subtrees on a tree with maximum degree 4 for such a given graph. This is a recognition algorithm for [4, 4, 2] graphs.

Original language | English |
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Pages (from-to) | 2031-2047 |

Number of pages | 17 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 9 |

DOIs | |

State | Published - 6 May 2009 |

## Keywords

- Edge intersection graph of subtrees on a tree
- Weakly chordal graph

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics