Connectivity in Matroids
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1301-1324
Voir la notice de l'article provenant de la source Cambridge University Press
An edge of a 3-connected graph G is called essential if the 3-connection of G is destroyed both when the edge is deleted and when it is contracted to a single vertex. It is known (1) that the only 3-connected graphs in which every edge is essential are the “wheel-graphs.” A wheel-graph of order n, where n is an integer ⩾3, is constructed from an n-gon called its “rim” by adding one new vertex, called the “hub,” and n new edges, or “spokes” joining the new vertex to the n vertices of the rim; see Figure 4A.A matroid can be regarded as a generalized graph. One way of developing the theory of matroids is therefore to generalize known theorems about graphs. In the present paper we do this with the theorem stated above.
Tutte, W. T. Connectivity in Matroids. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1301-1324. doi: 10.4153/CJM-1966-129-2
@article{10_4153_CJM_1966_129_2,
author = {Tutte, W. T.},
title = {Connectivity in {Matroids}},
journal = {Canadian journal of mathematics},
pages = {1301--1324},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-129-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-129-2/}
}
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