## Abstract

A matching is a set of edges without common endpoint. It was recently shown that every 1-planar graph (i.e., a graph that can be drawn in the plane with at most one crossing per edge) that has minimum degree 3 has a matching of size at least n+127 , and this is tight for some graphs. The proof did not come with an algorithm to find the matching more efficiently than a general-purpose maximum-matching algorithm. In this paper, we give such an algorithm. More generally, we show that any matching that has no augmenting paths of length 9 or less has size at least n+127 in a 1-planar graph with minimum degree 3.

F. Klute—This work was conducted while FK was a member of the “Algorithms and Complexity Group” at TU Wien.

Research of TB supported by NSERC. Research initiated while FK was visiting the University of Waterloo.

F. Klute—This work was conducted while FK was a member of the “Algorithms and Complexity Group” at TU Wien.

Research of TB supported by NSERC. Research initiated while FK was visiting the University of Waterloo.

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science |

Subtitle of host publication | 46th International Workshop, WG 2020, Leeds, UK, June 24–26, 2020, Revised Selected Papers |

Editors | Isolde Adler, Haiko Müller |

Publisher | Springer |

Pages | 248-260 |

Number of pages | 13 |

ISBN (Electronic) | 978-3-030-60440-0 |

ISBN (Print) | 978-3-030-60439-4 |

DOIs | |

Publication status | Published - 2020 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 12301 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |