## Abstract

A matching M in a graph G is uniquely restricted if no other matching in G covers the same set of vertices. We conjecture that every connected subcubic graph with m edges and b bridges that is distinct from K _{3,3} has a uniquely restricted matching of size at least m/+b6, and we establish this bound with b replaced by the number of bridges that lie on a path between two vertices of degree at most 2. Moreover, we prove that every connected subcubic graph of order n and girth at least 7 has a uniquely restricted matching of size at least n/−13, which partially confirms a conjecture of Fürst and Rautenbach (Graphs Combin. 35 (2019) 353–361).

Original language | English |
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Pages (from-to) | 189-194 |

Number of pages | 6 |

Journal | Discrete Applied Mathematics |

Volume | 262 |

DOIs | |

Publication status | Published - 15 Jun 2019 |

## Keywords

- Bridge
- Girth
- Matching
- Subcubic
- Uniquely restricted matching

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics