The Broken-circuit Complex: Its Structure and Factorizations
In this paper we derive several structural results for the broken-circuit complex of a combinatorial geometry G. In particular, motivated by the question as to when the characteristic polynomial of G factors, we investigate when the broken-circuit complex has a non-trivial join decomposition, conjecturing that such a decomposition cannot occur unless G has a non-trivial modular flat. © 1980, Academic Press Inc. (London) Limited. All rights reserved.
Publication Source (Journal or Book title)
European Journal of Combinatorics
Brylawski, T., & Oxley, J. (1981). The Broken-circuit Complex: Its Structure and Factorizations. European Journal of Combinatorics, 2 (2), 107-121. https://doi.org/10.1016/S0195-6698(81)80001-7