# On factors of 4-connected claw-free graphs

Broersma, H.J.
and
Kriesell, M.
and
Ryjacek, Z.
(2001)
*On factors of 4-connected claw-free graphs.*
Journal of Graph Theory, 37
(2).
pp. 125-136.
ISSN 0364-9024

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Abstract: | We consider the existence of several different kinds of factors in 4-connected claw-free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4-connected line graph is hamiltonian, i.e., has a connected 2-factor. Conjecture 2 (Matthews and Sumner): Every 4-connected claw-free graph is hamiltonian. We first show that Conjecture 2 is true within the class of hourglass-free graphs, i.e., graphs that do not contain an induced subgraph isomorphic to two triangles meeting in exactly one vertex. Next we show that a weaker form of Conjecture 2 is true, in which the conclusion is replaced by the conclusion that there exists a connected spanning subgraph in which each vertex has degree two or four. Finally we show that Conjectures 1 and 2 are equivalent to seemingly weaker conjectures in which the conclusion is replaced by the conclusion that there exists a spanning subgraph consisting of a bounded number of paths. |

Item Type: | Article |

Copyright: | © 2001 Wiley InterScience |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/71757 |

Official URL: | https://doi.org/10.1002/jgt.1008 |

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Metis ID: 201534