2012/12/31 by Jérémie Chalopin, Victor Chepoi, Damian Osajda · 1 citation
Mathematics · Computer Science · #math.CO #cs.DM #msc:05B35 #msc:05C12 #msc:57M10 #msc:57M20
paper · pdf · doi:10.1016/j.jctb.2015.03.004
published as Journal of Combinatorial Theory, Series B 114 (2015) 1-32 · 28 pages
arxiv created 2015/03/24 · arxiv updated 2018/12/10
We characterize 2-dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer (Conjecture 3 of S. Maurer, Matroid basis graphs I, JCTB 14 (1973), 216-240). We also establish Conjecture 1 from the same paper about the redundancy of the conditions in the characterization of basis graphs. We indicate positive-curvature-like aspects of the local properties of the studied complexes. We characterize similarly the corresponding 2-dimensional complexes of even Δ-matroids.