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Blocking set
In geometry, specifically projective geometry, a blocking set is a set of points in a projective plane which every line intersects and which does not contain an entire line. The concept can be generalized in several ways. Instead of talking about points and lines, one could deal with ''n''-dimensional subspaces and ''m''-dimensional subspaces, or even more generally, objects of type 1 and objects of type 2 when some concept of intersection makes sense for these objects. A second way to generalize would be to move into more abstract settings than projective geometry. One can define a blocking set of a hypergraph as a set that meets all edges of the hypergraph.
== Definition ==
In a finite projective plane π of order ''n'', a blocking set is a set of points of π which every line intersects and which contains no line completely. Under this definition, if ''B'' is a blocking set, then complementary set of points, π\''B'' is also a blocking set. A blocking set ''B'' is ''minimal'' if the removal of any point of ''B'' leaves a set which is not a blocking set. A blocking set of smallest size is called a ''committee''. Every committee is a minimal blocking set, but not all minimal blocking sets are committees. Blocking sets exist in all projective planes except for the smallest projective plane of order 2, the Fano plane.
It is sometimes useful to drop the condition that a blocking set does not contain a line. Under this extended definition, and since, in a projective plane every pair of lines meet, every line would be a blocking set. Blocking sets which contained lines would be called ''trivial'' blocking sets.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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