论文标题
II类图形分解为两个I类图形
Decomposition of class II graphs into two class I graphs
论文作者
论文摘要
Mkrtchyan和Steffen [J。 Graph Doemon，70（4），473--482，2012]表明，每个II类简单的图形都可以分解为最大$δ$ - edge-gedgo-gesso-edgo-golable-golable-grolable-grolable子图和匹配。他们进一步推测，每个图形$ g $带有色素索引$δ（g）+k $（$ k \ geq 1 $）可以分解为最大$δ（g）$ - $ - edge-edge-enge-edge-edrableable-exch-colorable-able-exch-colorable子图（不一定是$ k $ - $ k $ - edge-edge-edge-edge-edge-edge-edbleable-enge-colorable-colorable-colorable-colobable suberphaph。在本文中，我们首先将它们的结果推广到多编码，并表明每个具有多重$μ$ $的多数$ g $可以分解为最大$δ（g）$ - $ - edge-edge-edrableable-enge-edge-edrableable-graphable子图和最高学位的子图。然后，我们证明，每个图形$ g $带有色素索引$δ（g）+k $可以分解为两个I类子图$ H_1 $和$ H_2 $，因此$δ（H_1）=δ（g）$和$δ（h_2）= k $，这是他们猜想的各种。
Mkrtchyan and Steffen [J. Graph Theory, 70 (4), 473--482, 2012] showed that every class II simple graph can be decomposed into a maximum $Δ$-edge-colorable subgraph and a matching. They further conjectured that every graph $G$ with chromatic index $Δ(G)+k$ ($k\geq 1$) can be decomposed into a maximum $Δ(G)$-edge-colorable subgraph (not necessarily class I) and a $k$-edge-colorable subgraph. In this paper, we first generalize their result to multigraphs and show that every multigraph $G$ with multiplicity $μ$ can be decomposed into a maximum $Δ(G)$-edge-colorable subgraph and a subgraph with maximum degree at most $μ$. Then we prove that every graph $G$ with chromatic index $Δ(G)+k$ can be decomposed into two class I subgraphs $H_1$ and $H_2$ such that $Δ(H_1) = Δ(G)$ and $Δ(H_2) = k$, which is a variation of their conjecture.
