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For each rational number q \geq 1, we describe two partitions of the vertex set of a graph G, called the q-brick partition and the q-superbrick partition. The special cases when q=1 are the partitions given by the connected components and the 2-edge-connected components of G, respectively. We obtain structural results on these partitions and describe their relationship to the principal partitions of a matroid.
Bibtex entry:
| AUTHOR | = | {Jackson, Bill and Jord{\'a}n, Tibor}, |
| TITLE | = | {Brick Partitions of Graphs}, |
| NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2007}, |
| NUMBER | = | {TR-2007-05} |