Colour degree matrices of graphs with at most one cycle

© 2015 Elsevier B.V. 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.