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math.CO2014
Cycles in Oriented 3-graphs
Imre Leader, Ta Sheng Tan
An oriented 3-graph consists of a family of triples (3-sets), each of which is given one of its two possible cyclic orientations. A cycle in an oriented 3-graph is a positive sum o…
math.CO2014
Connected Colourings of Complete Graphs and Hypergraphs
Imre Leader, Ta Sheng Tan
Gallai's colouring theorem states that if the edges of a complete graph are 3-coloured, with each colour class forming a connected (spanning) subgraph, then there is a triangle tha…