Lower Bounds on the Probability of Connectedness in Classes of Random Graphs Generated by 2-Connected Graphs with a Given Base Spectrum

We develop a previous result which claims that the base spectrum of the cycle matroid of a graph provides a lower bound on the probability of connectedness of the corresponding random graph. A random graph with a minimum probability of connectedness is constructed in the class of random graphs generated by 2-connected graphs representable as a partition of their two trees.