%0 Journal Article %J The Electronic Journal of Combinatorics %D 2012 %T Non-Recursively Constructible Recursive Families of Graphs %A Colleen Bouey %A Christina Graves %A Aaron Ostrander %A Gregory Palma %X In a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjecture, which we then extend to an infinite family of counterexamples. %B The Electronic Journal of Combinatorics %V 19 %8 2012/04/16 %G eng %U http://www.combinatorics.org/ojs/index.php/eljc/article/view/2211 %N 2