Four results about self-blocking clutters Original Research Article

In this paper we introduce a new operator on self-blocking clutters (SBCs). Simpler than the median operator, it allows small modifications between SBCs. Thanks to this operator we design an algorithm which embeds without new vertex (when possible) an intersecting clutter in an SBC; and we provide the set of finite SBCs with a structure of connected graph. The two other results do not use the operator. One proves the nonexistence of good colourings for SBCs and characterizes the τ-critical SBCs. We conclude with an open question.