Highly connected hypergraphs containing no two edge-disjoint spanning connected subhypergraphs

The edge-connectivity of a connected graph or hypergraph is the minimum number of edges whose removal renders the graph or hypergraph, respectively, disconnected. The edge-connectivity of a (hyper) graph cannot exceed its minimum degree. For graphs, ...

Let $$k\ge 2, p\ge 1, q\ge 0$$kź2,pź1,qź0 be integers. We prove that every $$(4kp-2p+2q)$$(4kp-2p+2q)-connected graph contains p spanning subgraphs $$G_i$$Gi for $$1\le i\le p$$1≤i≤p and q spanning trees such that all $$p+q$$p+q subgraphs are pairwise ...

Finding edge-disjoint odd cycles is one of the most important problems in graph theory, graph algorithms and combinatorial optimization. One of the difficulties of this problem is that the Erd s-Pósa property does not hold for odd cycles in general. ...