The Hamilton‐Waterloo problem for Hamilton cycles and triangle‐factors

Abstract In this article, we consider the Hamilton‐Waterloo problem for the case of Hamilton cycles and triangle‐factors when the order of the complete graph Kn is even. We completely solved the problem for the case n≡24 (mod 36). For the cases n≡0 (mod 18) and n≡6 (mod 36), we gave an almost complete solution. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 305–316, 2012