Probabilities of Sentences about Very Sparse Random Graphs

James F. Lynch
1992 Random structures & algorithms (Print)  
W e consider random graphs with edge probability Pn-Q, where n is the number of vertices of the graph, / 3 > 0 is fixed, and a = 1 or a = (I + 1)/1 for some fixed positive integer I . We prove that for every firstorder sentence, the probability that the sentence is true for the random graph has an asymptotic limit. Also, there is an eflective procedure for generating the value of the limit in closed form.
doi:10.1002/rsa.3240030105 fatcat:jctrrksmsffrzfpzwpd2ifqik4