Let \(K_n\) 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 \(K_n\), denoted by \({\mathcal {T}}^d_{i}(K_n)\), as the smallest integer k such that there is an edge-covering of \(K_n\) by k “plane” hypergraphs of degree at most d and size of edge bounded by i. We compute this number for graphs (that is \(i=2\)) and gives some bounds for general hypergraphs.
['Clément Charpentier', 'Sylvain Gravier', 'Thomas Lecorre']
Trinque problem: covering complete graphs by plane degree-bounded hypergraphs