κ-path-connectivity and mk-generation: an Upper Bound on m
M. Abreu, Stephen C. Locke · Birkhäuser Basel eBooks · 2006
We consider simple connected graphs for which there is a path of length at least κ between every pair of distinct vertices. We wish to show that in these graphs the cycle space over ℤ 2 is generated by the cycles of length at least mk , where m = 1 for 3 ≤ κ ≤ 6, m = 6/7 for κ = 7, m ≥ 1/2 for κ ≥ 8 and m ≤ 3/4 + o (1) for large k.