Common transversals Export

@article{citeulike:4522283, abstract = {Given t families, each family consisting of s finite sets, we show that if the families ” separate points” in a natural way, and if the union of all the sets in all the families contains more than ( s + 1) t − s t −1 − 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is s t − s t −1 . Both of these bounds are best possible. This work extends recent work of Longyear [2].}, author = {Brown, T.}, citeulike-article-id = {4522283}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0097-3165(76)90048-0}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/0097316576900480}, doi = {10.1016/0097-3165(76)90048-0}, issn = {00973165}, journal = {Journal of Combinatorial Theory, Series A}, keywords = {transversals}, month = {July}, number = {1}, pages = {80--85}, posted-at = {2009-05-15 09:07:43}, priority = {2}, title = {Common transversals}, url = {http://dx.doi.org/10.1016/0097-3165(76)90048-0}, volume = {21}, year = {1976} }

TY - JOUR ID - citeulike:4522283 L3 - citeulike-article-id:4522283 N2 - Given t families, each family consisting of s finite sets, we show that if the families “separate points” in a natural way, and if the union of all the sets in all the families contains more than ( s + 1) t − s t −1 − 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is s t − s t −1 . Both of these bounds are best possible. This work extends recent work of Longyear [2]. IS - 1 JF - Journal of Combinatorial Theory, Series A SN - 00973165 EP - 85 TI - Common transversals VL - 21 SP - 80 KW - transversals AU - Brown, T PY - 1976/07// UR - http://dx.doi.org/10.1016/0097-3165(76)90048-0 ER -