Extending Hall's Theorem into List Colorings: A Partial History
In 1988, A. J. W. Hilton and P. D. Johnson Jr. found a natural generalization of the condition in Philip Hall's celebrated theorem on systems of distinct representatives. This generalization was formed in the relatively new theory of list colorings of graphs. Here we give an account of a strand...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/72168 |
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| Summary: | In 1988, A. J. W. Hilton and P. D. Johnson Jr. found a natural generalization of the condition in Philip Hall's celebrated theorem on systems of distinct representatives. This generalization was formed in the relatively new theory of list colorings of graphs. Here we give an account of a strand of development arising from this
generalization, concentrating on extensions of Hall's theorem. New results are presented concerning list colorings of independence systems and colorings of graphs with nonnegative measurable functions on positive measure spaces. |
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| ISSN: | 0161-1712 1687-0425 |