Formation of the first ring structure from small aliphatic molecules is often regarded as the rate-determining step (and in any case as a step of paramount importance) in the combustive growth of larger aromatic systems and soot lamellae. Among possible reactions able to start off this process, the radical addition of the propargyl radical to butadiyne (diacetylene) has been recently studied theoretically [G. da Silva, A. Trevitt, Phys. Chem. Chem. Phys. 13 (2011) 8940] and shown to lead preferentially to a 5-membered ring intermediate. The same reaction is here addressed focusing instead on the possible formation of 6-membered rings. The large variety of partially intertwined reaction pathways is the basis for a subsequent RRKM study (carried out at different combustion temperatures). It confirms, on one hand, the favored formation of fulvenallenyl radical indicated by da Silva and Trevitt, but also indicates the possible formation of six-membered cyclic systems as minor products. In particular, at high pressure, six-membered ring system yields are very low, but at lower pressures a more significant yield of six-membered ring product is predicted. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.