TY - JOUR
T1 - A general criterion for the existence of transversals
AU - Aharoni, R.
AU - Nash-Williams, C. S.J.A.
AU - Shelah, S.
PY - 1983/7
Y1 - 1983/7
N2 - We present a necessary and sufficient condition for a family of sets to possess a transversal. Its form follows that of P. Hall’s theorem: a family has a transversal if and only if it does not contain one of a set of ‘forbidden’ substructures.
AB - We present a necessary and sufficient condition for a family of sets to possess a transversal. Its form follows that of P. Hall’s theorem: a family has a transversal if and only if it does not contain one of a set of ‘forbidden’ substructures.
UR - http://www.scopus.com/inward/record.url?scp=0013465419&partnerID=8YFLogxK
U2 - 10.1112/plms/s3-47.1.43
DO - 10.1112/plms/s3-47.1.43
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AN - SCOPUS:0013465419
SN - 0024-6115
VL - S3-47
SP - 43
EP - 68
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
IS - 1
ER -