论文标题
Stiebitz型的概括在图分解上结果
A generalization of Stiebitz-type results on graph decomposition
论文作者
论文摘要
在本文中，我们考虑了在最低程度约束下多编码的分解，并对各种研究人员进行了几个结果的统一概括。令$ g $是一个多式印象，其中没有四角形和其他四边形的边缘，让$μ_g（v）= \ max \ {μ_g（u，v）：u \ in v（g）\ setMinus \ setMinus \ setMinus \ \ {v \} $ us $ us $ us $ u us us us us us us us us us us us us us us us us u u u u u u u u u u u u u u u u u u u u u，在$ g $中。我们表明，对于任何两个函数，$ a，b：v（g）\ rightarrow \ mathbb {n} \ setminus \ {0,1 \} $，如果$ d_g（v）\ ge a（v）+ge a（v）+b（v）+b（v）+2μ___________________________________3$ for v in v in v in v in v in v（y） $ d_x（x）\ geq a（x）$ in x $中的每个$ x \ and $ d_y（y）\ geq b（y）$ in y $ in y $ in y $。这是由于Diwan [3]，Liu和Xu [7]以及MA和Yang [10]在简单图上扩展到多编码设置的相关结果。
In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let $G$ be a multigraph in which no quadrilaterals share edges with triangles and other quadrilaterals and let $μ_G(v)=\max\{μ_G(u,v):u\in V(G)\setminus\{v\}\}$, where $μ_G(u,v)$ is the number of edges joining $u$ and $v$ in $G$. We show that for any two functions $a,b:V(G)\rightarrow\mathbb{N}\setminus\{0,1\}$, if $d_G(v)\ge a(v)+b(v)+2μ_G(v)-3$ for each $v\in V(G)$, then there is a partition $(X,Y)$ of $V(G)$ such that $d_X(x)\geq a(x)$ for each $x\in X$ and $d_Y(y)\geq b(y)$ for each $y\in Y$. This extends the related results due to Diwan [3], Liu and Xu [7] and Ma and Yang [10] on simple graphs to the multigraph setting.
