Trinque problem: covering complete graphs by plane degree-bounded hypergraphs

Clément Charpentier, Sylvain Gravier () and Thomas Lecorre
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Clément Charpentier: Université Joseph Fourier / CNRS, UMR 5582
Sylvain Gravier: Université Joseph Fourier / CNRS, UMR 5582
Thomas Lecorre: Université Joseph Fourier / CNRS, UMR 5582

Journal of Combinatorial Optimization, 2017, vol. 33, issue 2, No 10, 543-550

Abstract: Abstract Let $$K_n$$ 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 $$K_n$$ K n , denoted by $${\mathcal {T}}^d_{i}(K_n)$$ T i d ( K n ) , as the smallest integer k such that there is an edge-covering of $$K_n$$ 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 $$i=2$$ i = 2 ) and gives some bounds for general hypergraphs.

Keywords: Plane hypergraph; Edge covering; Complete graphs; Edge partition (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-015-9978-3

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