## Abstract

Let α^{′}(G) be the matching number of a graph G. A characterization of the graphs with given maximum odd degree and smallest possible matching number is given by Henning and Shozi (2021) [13]. In this paper we complete our study by giving a characterization of the graphs with given maximum even degree and smallest possible matching number. In 2018 Henning and Yeo [10] proved that if G is a connected graph of order n, size m and maximum degree k where k≥4 is even, then [Formula presented], unless G is k-regular and n∈{k+1,k+3}. In this paper, we give a complete characterization of the graphs that achieve equality in this bound when the maximum degree k is even, thereby completing our study of graphs with given maximum degree and smallest possible matching number.

Original language | English |
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Article number | 112731 |

Journal | Discrete Mathematics |

Volume | 345 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2022 |

## Keywords

- Factor-critical
- Matching number
- Maximum degree

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics