Brick partitions of graphs

Bill Jackson, Tibor Jordán

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

For each rational number q = b / c where b ≥ c are positive integers, we define a q-brick of G to be a maximal subgraph H of G such that c H has b edge-disjoint spanning trees, and a q-superbrick of G to be a maximal subgraph H of G such that c H - e has b edge-disjoint spanning trees for all edges e of c H, where c H denotes the graph obtained from H by replacing each edge by c parallel edges. We show that the vertex sets of the q-bricks of G partition the vertex set of G, and that the vertex sets of the q-superbricks of G form a refinement of this 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.

Original languageEnglish
Pages (from-to)270-275
Number of pages6
JournalDiscrete Mathematics
Volume310
Issue number2
DOIs
Publication statusPublished - Jan 28 2010

Keywords

  • Bricks and superbricks
  • Edge-disjoint spanning trees
  • Principal partitions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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