(1, 2)-Factorizations of General Eulerian Nearly Regular Graphs

Abstract

Every general graph with degrees 2k and 2k − 2, k ≥ 3, with zero or at least two vertices of degree 2k − 2 in each component, has a k-edge-colouring such that each monochromatic subgraph has degree 1 or 2 at every vertex.In particular, if T is a triangle in a 6-regular general graph, there exists a 2-factorization of G such that each factor uses an edge in T if and only if T is non-separating.