Extending the disjoint-representatives theorems of Hall, Halmos, and Vaughan to list-multicolorings of graphs

@article{Cropper2000ExtendingTD,
  title={Extending the disjoint-representatives theorems of Hall, Halmos, and Vaughan to list-multicolorings of graphs},
  author={Matthew M. Cropper and John L. Goldwasser and Anthony J. W. Hilton and Dean G. Hoffman and Peter D. Johnson},
  journal={Journal of Graph Theory},
  year={2000},
  volume={33},
  pages={199-219}
}
Philip Hall’s famous theorem on systems of distinct representatives and its not-so-famous improvement by Halmos and Vaughan (1950) can be regarded as statements about the existence of proper list-colorings or listmulticolorings of complete graphs. The necessary and sufficient condition for a proper “coloring” in these theorems has a rather natural… CONTINUE READING