The Pancyclicity of Halin Graphs and their Exterior Contractions

A new class of graphs called skirted graphs is introduced and it is shown that they are almost pancyclic. From this it is shown that Halin graphs and graphs obtained from Halin graphs by contracting only one exterior edge are pancyclic. In addition, the conjecture of Malkevitch that every regular Halin graph of degree at least four is pancyclic is answered in the affirmative.