Decomposing multigraphs into two Class I subgraphs with prescribed maximum degrees

Yonglei Chen, Yan Cao

Let $G$ be a finite loopless multigraph with maximum degree $\Delta$ and ${\chi }^{\prime }(G)=\Delta +k$, where $k\ge 0$. We prove that for every pair of positive integers $p,q$ satisfying $$p+q=Δ+k\qquad\t…