Let $\Gamma$ be a connected graph with $H^1(\Gamma) \cong \mathbb{Z}^d$. Can we give a lower bound (preferably of the form $\gg d$) on the maximal number of edge-disjoint cycles one can find in $\Gamma$?
Number of edge-disjoint cycles in a holey graph
H A Helfgott
- 20.2k
- 3
- 43
- 126