LAUSR

Let $$K_n$$Kn be a complete graph drawn on the plane with every vertex incident to the infinite face. For any integers i and d, we define the (i, d)-Trinque Number of $$K_n$$Kn, denoted by $${\mathcal {T}}^d_{i}(K_n)$$Tid(Kn), as the smallest integer k such that there is an edge-covering of $$K_n$$Kn by k “plane” hypergraphs of degree at most d and size of edge bounded by i. We compute this number for graphs (that is $$i=2$$i=2) and gives some bounds for general hypergraphs.