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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/72168 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556830550654976 |
|---|---|
| author | D. G. Hoffman P. D. Johnson |
| author_facet | D. G. Hoffman P. D. Johnson |
| author_sort | D. G. Hoffman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8d14c32b47d6451494e065c200f6519f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8d14c32b47d6451494e065c200f6519f2025-02-03T05:44:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/7216872168Extending Hall's Theorem into List Colorings: A Partial HistoryD. G. Hoffman0P. D. Johnson1Department of Mathematics and Statistics, Auburn University, Auburn 36849, AL, USADepartment of Mathematics and Statistics, Auburn University, Auburn 36849, AL, USAIn 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.http://dx.doi.org/10.1155/2007/72168 |
| spellingShingle | D. G. Hoffman P. D. Johnson Extending Hall's Theorem into List Colorings: A Partial History International Journal of Mathematics and Mathematical Sciences |
| title | Extending Hall's Theorem into List Colorings: A Partial History |
| title_full | Extending Hall's Theorem into List Colorings: A Partial History |
| title_fullStr | Extending Hall's Theorem into List Colorings: A Partial History |
| title_full_unstemmed | Extending Hall's Theorem into List Colorings: A Partial History |
| title_short | Extending Hall's Theorem into List Colorings: A Partial History |
| title_sort | extending hall s theorem into list colorings a partial history |
| url | http://dx.doi.org/10.1155/2007/72168 |
| work_keys_str_mv | AT dghoffman extendinghallstheoremintolistcoloringsapartialhistory AT pdjohnson extendinghallstheoremintolistcoloringsapartialhistory |