If the SNP falls short of an overall majority of seats in Holyrood, it will certainly hope for support from the Greens over an independence referendum, but there may also be talks between the two parties over a broader partnership.
The Greens have played a crucial role in helping the SNP government get its annual budgets passed by parliament – and won significant policy and spending shifts as a result.
Could the co-operation now go further and take the shape of a formal coalition, with Greens in the Cabinet?
Many European countries have already seen Greens in power as part of a coalition.
And, launching the party’s manifesto last week, co-leader Patrick Harvie suggested they would be willing to "have the conversation".
"We do aspire to take a role in government," he said, though he quickly added there were "really massive issues" the SNP was not yet grappling with – and he named the transition away from fossil fuels and the land reform agenda.
However, the Greens have been in the parliament since the start 22 years ago, have grown over that time, and are now firmly part of the political landscape.
“There is a point when you start to think what more could you do with more leverage,” says one party insider. "We have more experience now, we’re a bigger party, with more weight in terms of diversity of policy strengths and the manifesto is more substantial.”
But of course any coalition would depend on the arithmetic and what deal could be negotiated. Will the Greens have the numbers to make the difference if the SNP falls short of a majority?
And will it have enough MSPs to staff a coalition? Polling at round nine per cent, the Greens talk of getting a record 10 seats but are acutely aware a slight drop in that percentage can mean a bigger drop in MSP numbers.
And, as with any potential coalition, whatever policy concessions can be secured in talks would have to be weighed against the potential costs of being in government, having to take part in difficult decisions and make inevitable compromises. The smaller party in a coalition often pays a price later, as the Lib Dems found after their UK coalition with David Cameron’s Tories. But the Lib Dems were not harmed by their coalition with Labour for the first eight years of devolution, from 1999 to 2007, and they got some of their key policies passed into legislation, including a new voting system for council elections and stronger freedom of information laws than south of the border.
Tackling inequalities and climate change are likely to be high on the Greens’ agenda.
But how important is it for the SNP to have an ongoing majority? The party managed remarkably well without a coalition partner during its two spells of minority government.
And so long as the Greens back the necessary legislation on an independence referendum and are open to deals on budgets and other issues on a case-by-case budget, Nicola Sturgeon may decide incorporating the Greens – however willing – into her government is not essential.