On Tours that contain all Edges of a Hypergraph
On Tours that contain all Edges of a Hypergraph
Let $H$ be a $k$-uniform hypergraph, $k\geqslant 2$. By an Euler tour in $H$ we mean an alternating sequence $v_0,e_1,v_1,e_2,v_2,\ldots,v_{m-1},e_m,v_m=v_0$ of vertices and edges in $H$ such that each edge of $H$ appears in this sequence exactly once and $v_{i-1},v_i\in e_i$, $v_{i-1}\neq v_i$, for every $i=1,2,\ldots,m$. This is an obvious …