Percolation is a well-studied process in statistical physics, however there are only a handful of exact results for percolation transition on general graphs. In this talk I will present my recent work of constructing an lower bound for the bond percolation transition on an arbitrary graph, using eigenvalues of a matrix associated with the graph that I call triangle-non-backtracking matrix. This matrix is closely related to the linearization of the Belief Propagation equations (a.k.a. cavity method in statistical physics) incorporating triangles in the graph. Our bound is in general tighter than existing bounds, and becomes exact for an infinite graph with no loops longer than 3.