A Generalization of Stiebitz-Type Results on Graph Decomposition
نویسندگان
چکیده
In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization several results by various researchers. Let $G$ be multigraph in which no quadrilaterals share edges with triangles other let $\mu_G(v)=\max\{\mu_G(u,v):u\in V(G)\setminus\{v\}\}$, where $\mu_G(u,v)$ is number joining $u$ $v$ $G$. We show that for any two functions $a,b:V(G)\rightarrow\mathbb{N}\setminus\{0,1\}$, if $d_G(v)\ge a(v)+b(v)+2\mu_G(v)-3$ each $v\in V(G)$, then there partition $(X,Y)$ $V(G)$ such $d_X(x)\geq a(x)$ $x\in X$ $d_Y(y)\geq b(y)$ $y\in Y$. This extends related due to Diwan, Liu–Xu Ma–Yang on simple graphs setting.
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ژورنال
عنوان ژورنال: Electronic Journal of Combinatorics
سال: 2021
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/9757