### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 282-299 |

Number of pages | 18 |

Journal | Journal of graph theory |

Volume | 79 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2015 |

### Keywords

- MSC-05C
- METIS-314967
- IR-98274
- EWI-26316

### Cite this

*Journal of graph theory*,

*79*(4), 282-299. https://doi.org/10.1002/jgt.21832

}

*Journal of graph theory*, vol. 79, no. 4, pp. 282-299. https://doi.org/10.1002/jgt.21832

**Linear-time algorithms for scattering number and hamilton-connectivity of interval graphs.** / Broersma, Haitze J.; Fiala, Jiri; Golovach, Petr A.; Kaiser, Tomas; Paulusma, Daniël; Proskurowski, Andrzej.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Linear-time algorithms for scattering number and hamilton-connectivity of interval graphs

AU - Broersma, Haitze J.

AU - Fiala, Jiri

AU - Golovach, Petr A.

AU - Kaiser, Tomas

AU - Paulusma, Daniël

AU - Proskurowski, Andrzej

N1 - eemcs-eprint-26316

PY - 2015/8

Y1 - 2015/8

N2 - We prove that for all integers k<0 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an O(n+m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known O(n^3) time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(n+m) time.

AB - We prove that for all integers k<0 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an O(n+m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known O(n^3) time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(n+m) time.

KW - MSC-05C

KW - METIS-314967

KW - IR-98274

KW - EWI-26316

U2 - 10.1002/jgt.21832

DO - 10.1002/jgt.21832

M3 - Article

VL - 79

SP - 282

EP - 299

JO - Journal of graph theory

JF - Journal of graph theory

SN - 0364-9024

IS - 4

ER -