A conjecture of Welsh revisited

作者：McGuinness Sean^*

来源：European Journal of Combinatorics, 2010, 31(8): 2120-2129.

DOI：10.1016/j.ejc.2010.06.002

Welsh conjectured that for any simple regular connected matroid M. if each cocircuit has at least 1/2(r(M)+1) elements, then there is a circuit of size r(M) +1 This conjecture was proven by Hochstattler and Jackson in 1997. In this paper, we give a shorter proof of this conjecture based solely on matroid-theoretical arguments Let M be a simple, connected, regular matroid and let C is an element of C(M). where vertical bar C vertical bar <= min{r(M). 2d - 1} We show that if vertical bar C*vertical bar >= d >= 2. for all C* is an element of C*(M) where C boolean AND C* = theta.

• 出版日期2010-12