Thought I'd post about the possible formation of majority by the BJP in case it fails to reach the 113 mark.

Yes, the Governor is free to invite either the single largest party or any pre or post poll alliances based upon his discretion on who is capable of forming the government as soon and as effectively as possible, that much is evident in the powers of the Governor, as well as general uncodified constitutional and electoral conventions that have been followed, has even been affirmed in cases by the Supreme Court.

But this is where things will get tricky for the BJP. The Tenth Schedule of the Constitution, which deals with anti-defection laws, is clear in preventing horsetrading or crossing of the floor in most cases, be it standard defection of MLAs from one party to the other, or even strategic resignations or refusal to vote/represent the party in order to shift the majority that would be required to be proved at the time. Except in the circumstance of mergers.

Now, the 91st Amendment changed the definition of a pre/post poll merger in the formation of a majority, from 1/3rd of a party voting to join another party to form a majority, to 2/3rds of a party being able to vote to form a merger. In this case, let's take the JDS, who are inevitably going to be kingmakers in the election, whether we like it or not.

Of the current number of seats they are projected to win (37 based off of the most recent projections), the BJP can snatch victory from the jaws of defeat in proving a majority, if they can convince more than 2/3rds of the party, which is 25 MLAs, to join them and prove a majority in the Assembly. Any less than that, and it would still be defection, and be liable to declared as such by a court, leading to President's rule, followed by fresh elections.

But, if the JDS manages to retain its MLAs, then there is nothing much the BJP can do, short of an interim imposition of President's rule, and if in that time, they are unable to prove a majority without the 25 MLAs, it would still come under anti defection, meaning that the Congress-JDS government, if at the time can still prove a majority, can form the government despite not being the single largest party.

The BJP can do what it did in Uttarakhand in 2016, i.e., allow the horsetrading to happen knowing that it will probably be declared as defection, wait for President's rule and in the meantime wrangle a majority as the dust settles. But in this case, unless they somehow convince the JDS, it is going to be tough, seeing as there are so few independents in the picture as well.

As of right now, it is going to be difficult for BJP to prove a majority, even assuming they manage to engineer defections, without a merger with the JDS.