Classification of genus two knots which admit a (1,1) decomposition
  We describe the genus two knots which admit a genus one, one bridge position. These are divided into several families, one consists of vertical bandings of two genus one $(1,1)$-knots, other consists of vertical bandings of two cross cap number two 2-bridge knots, and the last one consists of genus two tunnel number one satellite knots. 
Mario Eudave-Mu\~noz, Fabiola Manjarrez-Gutierrez, Enrique   Ramirez-Losada
math.GT