### Abstract

Original language | English |
---|---|

Pages (from-to) | 24-52 |

Journal | Journal of Graph Theory |

Volume | 41 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 |

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*Journal of Graph Theory*,

*41*(1), 24-52. https://doi.org/10.1002/jgt.10046

}

*Journal of Graph Theory*, vol. 41, no. 1, pp. 24-52. https://doi.org/10.1002/jgt.10046

**On the "largeur d'arborescence''.** / Holst, van der, H.

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

TY - JOUR

T1 - On the "largeur d'arborescence''

AU - Holst, van der, H.

PY - 2002

Y1 - 2002

N2 - Let la(G) be the invariant introduced by Colin de Verdière [J. Comb. Theory, Ser. B., 74:121-146, 1998], which is defined as the smallest integer n0 such that G is isomorphic to a minor of Kn×T, where Kn is a complete graph on n vertices and where T is an arbitrary tree. In this paper, we give an alternative definition of la(G), which is more in terms of the tree-width of a graph. We give the collection of minimal forbidden minors for the class of graphs G with la(G)k, for k=2, 3. We show how this work on la(G) can be used to get a forbidden minor characterization of the graphs with (G)3. Here, (G) is another graph parameter introduced in the above cited paper.

AB - Let la(G) be the invariant introduced by Colin de Verdière [J. Comb. Theory, Ser. B., 74:121-146, 1998], which is defined as the smallest integer n0 such that G is isomorphic to a minor of Kn×T, where Kn is a complete graph on n vertices and where T is an arbitrary tree. In this paper, we give an alternative definition of la(G), which is more in terms of the tree-width of a graph. We give the collection of minimal forbidden minors for the class of graphs G with la(G)k, for k=2, 3. We show how this work on la(G) can be used to get a forbidden minor characterization of the graphs with (G)3. Here, (G) is another graph parameter introduced in the above cited paper.

U2 - 10.1002/jgt.10046

DO - 10.1002/jgt.10046

M3 - Article

VL - 41

SP - 24

EP - 52

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -