Text this: Generalization of two results of Hilton on total-colourings of a graph

  ______     ___      _  _     ______     _____  
 /_   _//   / _ \\   | \| ||  /_   _//   / ___// 
 `-| |,-   | / \ ||  |  ' ||   -| ||-    \___ \\ 
   | ||    | \_/ ||  | .  ||   _| ||_    /    // 
   |_||     \___//   |_|\_||  /_____//  /____//  
   `-`'     `---`    `-` -`   `-----`  `-----`