Timeline for Is there always a maximum anti-rectangle with a corner square?
Current License: CC BY-SA 3.0
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| Nov 15, 2013 at 16:57 | comment | added | The Masked Avenger | Arrange 4 domino tiles in a pinwheel. If anti rectangles were sets of points, I'd say the largest had 4 points. Since they are small squares and not points, is a maximal AR one with 5 squares? | |
| Nov 15, 2013 at 10:00 | comment | added | Nick Gill | You should have a look at the paper that the OP links to - it discusses rectangular covers, and in particular shows that, in general, there is a 'gap' between the size of a minimal cover, and the size of a maximal anti-rectangle. I fear this `gap' might fatally compromise the cover-approach... | |
| Nov 14, 2013 at 23:41 | comment | added | The Masked Avenger | DIt looks like the idea needs more work. A pinwheel type polygon permits a cycle in the graph, so perhaps a graph based on the corners of the rectangles in the reduced cover is needed. | |
| Nov 14, 2013 at 17:44 | comment | added | The Masked Avenger | Of course other details remain, such as insisting that union of a cover is contained in the polygon. I think if there is no degree 1 vertex, then there is a cycle, from which one might show there is a hole. | |
| Nov 14, 2013 at 17:35 | history | answered | The Masked Avenger | CC BY-SA 3.0 |