13 May, 2017
Sturgeon has explicitly ruled out doing any deals with the Tories, even though the SNP had two coalitions with Conservative councillors after the 2012 election.
But a recent surge in support for the Scottish Conservatives could make that success hard to repeat.
Following the local elections which saw the SNP come out as the largest party across Scotland's local authorities, the SNP leader warned Prime Minister Theresa May that her flirtation with Ukip voters in England to pursue a hard negotiating stance with the European Union will result in the "sacrifice of thousands of Scottish jobs".
Basing its calculations partly on "notional" results the BBC said the SNP were actually down by seven, but it didn't really matter: the SNP vote had held up, and held up well.
"For the next few years, perhaps more than ever before, Scotland needs strong voices to stand up and make our voice heard".
At first glance the SNP scored another remarkable success in last week's local elections.
Nationally, May's party gained more than 550 council seats and swept to shock victories in mayoralty contests in the West Midlands and Tees Valley.
Mr Cullinane said: "Our strong performance in North Ayrshire is down to our achievements in office, including the no cuts budget we set in March, and our municipal socialist vision of municipal bus services, a not-for-profit energy company and more council homes".
Four councils that quit the Convention of Scottish Local Authorities (COSLA) in a dispute over decision-making processes - Glasgow, Aberdeen, Renfrewshire and South Lanarkshire - are expected to rejoin at the COSLA convention at the end of June.
Ms Davidson said that across the country, people are "looking for this Scottish fightback against the SNP".
And this, I suggest, is a problem for the first minister. "We will not be a government that presides over food bank Britain or asks teachers to go on the school gates and collect funds to pay the teachers' wages", he said.
But in truth the two figures, the 32% the party won last week and the 50% it secured two years ago, are not directly comparable with each other.
In retrospect, Nicola Sturgeon pushing for a second independence referendum when she did has turned out to be an absolute gift for her bitterest foes.
Ms Sturgeon said the election results showed the SNP in the ascendency north of the border, with Tories and Labour "scrapping for second place".
Yet the task facing the SNP next month is to defend its remarkable success in winning 56 out of Scotland's 59 seats at the United Kingdom election in 2015, a success based not on winning a little less than a third of the vote, but on securing 50%.
Ms Davidson spent the day campaigning in Gordon, where Mr Salmond is the SNP's candidate.
The total turnout in the ward was 43.3 percent, an increase from the last local election in 2012 (34.85).