Abstract

In this paper, we introduce the notion of $\beta$-greedoids and discuss four basic constructions of $\beta$-greedoids namely, deletion, contraction, direct sum and ordered sum. We show that the operations of deletion and contraction commute and the direct sum and ordered sum of $\beta$-greedoids $G_{1}$ and $G_{2}$ are interval $\beta$-greedoids if and only if $G_{1}$ and $G_{2}$ are both interval $\beta$-greedoids. We also give a necessary and sufficient condition for the direct sum and ordered sum of balanced $\beta$-greedoids to be balanced.

Keywords: $\beta$-greedoid; basis; feasible; flat; density; direct sum; ordered sum.

MSC: 52C99

Pages:  343$-$350     

Volume  66 ,  Issue  4 ,  2014