Ji-Cheng Ma

Matching complements in subcubic graphs and a proof of the 3-Decomposition Conjecture

We prove the 3-Decomposition Conjecture: every finite connected cubic loopless multigraph decomposes into a spanning tree, a 2-regular subgraph, and a matching. The proof rests on a new theorem on matching complements in subcubic graphs. Let H be a finite connected bridgeless simple graph of maximum degree three, and l...