Franceschini, Gianni (2001) *Some New Results for k-Dense Trees: Graph Theory.* Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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## Abstract

Let k be a positive integer. A k-cycle is a connected graph in which each vertex has degree greater than k. A k-dense forest is a graph for which no subgraph is a k-cycle; if a k-dense forest is connected, then it is k-dense tree. A k-leaf is a vertex of a k-dense forest with degree less than or equal to k. Any k-dense forest has at least one k-leaf. If a k-leaf is removed, the resulting graph is still a k-dense forest. This fact is on the basis of another characterization of k-dense forests which make use of the concept of k-elimination, a particular ordering of removal for the vertices of a k-dense forest. In this paper, we study some new properties of the complete k-dense trees, a subclass of the one of k-dense trees. Such properties reveal some interesting relations between the class of complete k-dense trees and the widely studied class of k-trees.

Item Type: | Book |
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Uncontrolled Keywords: | graph theory, k-cycle, k-dense forest, k-dense tree, complete k-dense tree, k-elimination, k-tree, triangulated graphs, triangulated constituent, connectivity, k-connectivity, k-edge-connectivity, k-linked, core |

Subjects: | Area01 - Scienze matematiche e informatiche > INF/01 - Informatica |

Divisions: | Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA |

Depositing User: | dott.ssa Sandra Faita |

Date Deposited: | 22 Dec 2014 14:24 |

Last Modified: | 22 Dec 2014 14:24 |

URI: | http://eprints.adm.unipi.it/id/eprint/2060 |

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