Unavoidable minors of graphs of large type

Authors:
John Dittmann;Bogdan Oporowski
Affiliations:
Department of Mathematics, University of New Orleans, New Orleans, LA;Department of Mathematics, Louisiana State University, Baton Rouge, LA
Venue:
Discrete Mathematics
Year:
2002

Citing 3
Cited 0

Typical subgraphs of 3- and 4-connected graphs

Journal of Combinatorial Theory Series B
On infinite antichains of matroids

Journal of Combinatorial Theory Series B
Unavoidable minors of large 3-connected binary matroids

Journal of Combinatorial Theory Series B

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Abstract

In this paper, we study one measure of complexity of a graph, namely its type. The type of a graph G is defined to be the minimum number n such that there is a sequence of graphs G = G0, G1,..., Gn, where Gi is obtained by contracting one edge in or deleting one edge from each block of Gi-1, and where Gn is edgeless. We show that a 3-connected graph has large type if and only if it has a minor isomorphic to a large fan. Furthermore, we show that if a graph has large type, then it has a minor isomorphic to a large fan or to a large member of one of two specified families of graphs.