Reconstruction of locally finite connected graphs with two infinite wings (Q1182943)

A graph is \(p\)-coherent if it can be expressed as the union of a finite subgraph and \(p\) disjoint infinite subgraphs but cannot be expressed as the union of a finite subgraph and \(p+1\) disjoint infinite subgraphs. In a previous paper [J. Graph Theory 11, 497-505 (1987; Zbl 0652.05039)], the author proved that every locally finite connected \(p\)-coherent graph is reconstructible if \(p\geq 3\). Here the author proves the same result for \(p=2\).