<p><a href="https://arxiv.org/pdf/1908.03473.pdf" rel="nofollow noreferrer">Barder and Burkhardt</a> in 2019 proposed this approach to find MSTs in linear time given the non-MST edges are given in ascending order of their weights.</p>
Linear Time Algorithm For MST
<p>I was wondering if anyone can point to a linear time algorithm to find the MST of a graph when there is a small number of weights (I.e edges can only have 2 different weights).</p>

<p>I could not find anything on google other than Prim's, Kruskal's, Boruvka's none of which seem to have any properties that would reduce the run time in this special case. I'm guessing to make it linear time it would have to be some sort of modification of BFS (which finds the MST when the weights are uniform).</p>