Colour degree matrices of graphs with at most one cycle - Hillebrand, A; McDiarmid, C (Elsevier, 2015)
Colour degree matrix problems, also known as edge-disjoint realisation and edge packing problems, have connections for example to discrete tomography. Necessary and sufficient conditions are known for a demand matrix to be the colour degree matrix of an edge-coloured forest. We give necessary and sufficient conditions for a demand matrix to be realisable by a graph with at most one cycle.