N-free extensions of posets.Note on a theorem of P.A.Grillet
| dc.creator | Pouzet, Maurice | |
| dc.creator | Zaguia, Nejib | |
| dc.date | 2005-09-13 | |
| dc.date.accessioned | 2026-07-07T03:23:26Z | |
| dc.date.available | 2026-07-07T03:23:26Z | |
| dc.description | Let $S\_{N}(P)$ be the poset obtained by adding a dummy vertex on each diagonal edge of the $N$'s of a finite poset $P$. We show that $S\_{N}(S\_{N}(P))$ is $N$-free. It follows that this poset is the smallest $N$-free barycentric subdivision of the diagram of $P$, poset whose existence was proved by P.A. Grillet. This is also the poset obtained by the algorithm starting with $P\_0:=P$ and consisting at step $m$ of adding a dummy vertex on a diagonal edge of some $N$ in $P\_m$, proving that the result of this algorithm does not depend upon the particular choice of the diagonal edge choosen at each step. These results are linked to drawing of posets. | |
| dc.description | 7 pages, 4 pictures | |
| dc.identifier | https://arxiv.org/abs/cs/0509034 | |
| dc.identifier | http://arxiv.org/abs/cs/0509034 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/32940 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | I.1.2; I.4.10; I.5 | |
| dc.title | N-free extensions of posets.Note on a theorem of P.A.Grillet | |
| dc.type | text |