### Abstract

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

Pages (from-to) | 244-255 |

Number of pages | 12 |

Journal | Journal of graph theory |

Volume | 75 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2014 |

### Keywords

- EWI-24563
- MSC-05C
- Forbidden subgraph
- Hamiltonian graph
- Toughness
- t-Tough graph
- METIS-305860
- IR-89614
- 2K2-free graph

### Cite this

_{2}-free graphs.

*Journal of graph theory*,

*75*(3), 244-255. https://doi.org/10.1002/jgt.21734

}

_{2}-free graphs'

*Journal of graph theory*, vol. 75, no. 3, pp. 244-255. https://doi.org/10.1002/jgt.21734

**On toughness and hamiltonicity of 2K _{2}-free graphs.** / Broersma, Haitze J.; Patel, Viresh; Pyatkin, Artem.

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

TY - JOUR

T1 - On toughness and hamiltonicity of 2K2-free graphs

AU - Broersma, Haitze J.

AU - Patel, Viresh

AU - Pyatkin, Artem

N1 - eemcs-eprint-24563

PY - 2014/3

Y1 - 2014/3

N2 - The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields |A|/t components. Determining toughness is an NP-hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K2-free graphs, that is, graphs that do not contain two vertex-disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K2-free graphs.

AB - The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields |A|/t components. Determining toughness is an NP-hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K2-free graphs, that is, graphs that do not contain two vertex-disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K2-free graphs.

KW - EWI-24563

KW - MSC-05C

KW - Forbidden subgraph

KW - Hamiltonian graph

KW - Toughness

KW - t-Tough graph

KW - METIS-305860

KW - IR-89614

KW - 2K2-free graph

U2 - 10.1002/jgt.21734

DO - 10.1002/jgt.21734

M3 - Article

VL - 75

SP - 244

EP - 255

JO - Journal of graph theory

JF - Journal of graph theory

SN - 0364-9024

IS - 3

ER -

_{2}-free graphs. Journal of graph theory. 2014 Mar;75(3):244-255. https://doi.org/10.1002/jgt.21734