Extending Hall's Theorem into List Colorings: A Partial History

Hoffman, D. G.; Johnson, P. D.

doi:https://doi.org/10.1155/2007/72168

International Journal of Mathematics and Mathematical Sciences

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Review Article | Open Access

Volume 2007 | Article ID 072168 | https://doi.org/10.1155/2007/72168

Extending Hall's Theorem into List Colorings: A Partial History

D. G. Hoffman¹and P. D. Johnson¹

Academic Editor: Eugene H. Dshalalow

Received14 Sept 2006

Accepted12 Feb 2007

Published19 Apr 2007

Abstract

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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Copyright

Copyright © 2007 D. G. Hoffman and P. D. Johnson Jr. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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