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The edge set of Kn cannot be decomposed into edge-disjoint hexagons (or 6-cycles) when n =1= 1 or 9 (mod 12). We discuss adding edges to the edge set of Kn so that the resulting graph can be decomposed into edge-disjoint hexagons. This paper gives the solution to this minimum covering of Kn with hexagons problem. A hexagon system is a pair (5, H) where H is… (More)

A complete solution of the maximum packing problem of Kn with hexagons is given. A hexagon system is a pair (S, H) where H is a collection of edge-disjoint hexagons which partition the edge set of the complete undirected graph Kn with vertex set S. The number lSI n is called the order of the hexagon system (S, H) and IHI = n(n-1)/12. In what follows we will… (More)

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