A special case says that, for each natural number k, every (12k − 7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.
A special case says that, for each natural number k, every(12k − 7)-edge-connected graph with an even number ofvertices contains a spanning subgraph in which each vertexhas degree congruent to k modulo 2k.