Some applications of the Nash-Williams lemma to the edge-reconstruction conjecture (Q914704)

A simple graph G is called fourdegreed if the cardinality of its degree set D(G) is four. It is shown that every fourdegreed graph is edge- reconstructible if either \(\delta\geq 8\) or \(d\geq \log_ 268\), where \(\delta\) and d are the minimum and average degree, respectively.