A helly number for unions of two boxes in R2
Let S be a polygonal region in the plane with edges parallel to the coordinate axes. If every 5 or fewer boundary points of S can be partitioned into sets A and B so that conv A⋃ conv B⫅S, then S is a union of two convex sets, each a rectangle. The number 5 is best possible.
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000291 |
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| _version_ | 1832562013323132928 |
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| author | Marilyn Breen |
| author_facet | Marilyn Breen |
| author_sort | Marilyn Breen |
| collection | DOAJ |
| description | Let S be a polygonal region in the plane with edges parallel to the coordinate axes. If every 5 or fewer boundary points of S can be partitioned into sets A and B so that conv A⋃ conv B⫅S, then S is a union of two convex sets, each a rectangle. The number 5 is best possible. |
| format | Article |
| id | doaj-art-d9a9d39b541845c89f0a108087003368 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d9a9d39b541845c89f0a1080870033682025-02-03T01:23:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018226727310.1155/S0161171285000291A helly number for unions of two boxes in R2Marilyn Breen0Department of Mathematics, University of Oklahoma, Norman 73019, Oklahoma, USALet S be a polygonal region in the plane with edges parallel to the coordinate axes. If every 5 or fewer boundary points of S can be partitioned into sets A and B so that conv A⋃ conv B⫅S, then S is a union of two convex sets, each a rectangle. The number 5 is best possible.http://dx.doi.org/10.1155/S0161171285000291Helly-type theoremsunions of convex sets. |
| spellingShingle | Marilyn Breen A helly number for unions of two boxes in R2 International Journal of Mathematics and Mathematical Sciences Helly-type theorems unions of convex sets. |
| title | A helly number for unions of two boxes in R2 |
| title_full | A helly number for unions of two boxes in R2 |
| title_fullStr | A helly number for unions of two boxes in R2 |
| title_full_unstemmed | A helly number for unions of two boxes in R2 |
| title_short | A helly number for unions of two boxes in R2 |
| title_sort | helly number for unions of two boxes in r2 |
| topic | Helly-type theorems unions of convex sets. |
| url | http://dx.doi.org/10.1155/S0161171285000291 |
| work_keys_str_mv | AT marilynbreen ahellynumberforunionsoftwoboxesinr2 AT marilynbreen hellynumberforunionsoftwoboxesinr2 |