RECONSTRUCTION OF POSETS WITH THE SAME COMPARABILITY GRAPH

Authors
ILLE P RAMPON JX
Citation
P. Ille et Jx. Rampon, RECONSTRUCTION OF POSETS WITH THE SAME COMPARABILITY GRAPH, J COMB TH B, 74(2), 1998, pp. 368-377
Citations number
12
Categorie Soggetti
Mathematics,Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES B
ISSN journal
00958956 → ACNP
Volume
74
Issue
2
Year of publication
1998
Pages
368 - 377
Database
ISI
SICI code
0095-8956(1998)74:2<368:ROPWTS>2.0.ZU;2-I
Abstract
Given two finite posets P and P' with the same comparability graph, we show that if \V(P)\ greater than or equal to 4 and if for all x is an element of V(P), P - x similar or equal to P' - x, then P similar or equal to P'. This result leads us to characterize the finite posets P such that for all x is an element of V(P), P - x similar or equal to P - x. (C) 1998 Academic Press.