Deltas, delta minors and delta free clutters
نویسندگان
چکیده
For an integer n ≥ 3, the clutter ∆n := { {1, 2}, {1, 3}, . . . , {1, n}, {2, 3, . . . , n} } is called a delta of dimension n, whose members are the lines of a degenerate projective plane. In his seminal paper on non-ideal clutters, Alfred Lehman manifested the role of the deltas as a distinct class of minimally non-ideal clutters [DIMACS, 1990]. A clutter is delta free if it has no delta minor. Binary clutters, ideal clutters and clutters with the packing property are examples of delta free clutters. In this paper, after introducing and studying basic geometric notions defined on clutters, we will investigate the surprising geometric attributes of the deltas, delta minors and delta free clutters. We will also state some conjectures on identically self-blocking clutters.
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