Potentially 2-connected integer pair sequences (Q1088689)

This paper deals with topics concerning edge sequences and their realizations, which were treated for example in \textit{A. N. Patrinos'} and \textit{S. L. Hakimi}'s joint paper in Discrete Math. 15, 347-358 (1976; Zbl 0328.05139), \textit{N. Achuthan}'s paper in Combinatorics and graph theory, Proc. Symp., Calcutta 1980, Lect. Notes Math. 885, 153-164 (1981; Zbl 0481.05058), or in the author's paper in Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 1982, No.3, 43-47 (1982; Zbl 0499.05050). In this paper the author solves the problem of characterization of potentially 2-connected edges sequences by giving a polynomial algorithm for verifying the potential 2-connectivity of an edge sequence and by proving an existence theorem for potentially 2-connected edge sequences. He finishes his paper by formulating a hypothesis on edge sequences being potentially n-connected (n\(\geq 2)\).