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 $\mu_G(v)=\max\{\mu_G(u,v):u\in V(G)\setminus\{v\}\}$, where $\mu_G(u,v)$ 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 $d_G(v)\ge a(v)+b(v)+2\mu_G(v)-3$ 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, Liu–Xu and Ma–Yang on simple graphs to the multigraph setting.
@article{10_37236_9757,
author = {Qinghou Zeng and Chunlei Zu},
title = {A generalization of {Stiebitz-type} results on graph decomposition},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/9757},
zbl = {1475.05153},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9757/}
}
TY - JOUR
AU - Qinghou Zeng
AU - Chunlei Zu
TI - A generalization of Stiebitz-type results on graph decomposition
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9757/
DO - 10.37236/9757
ID - 10_37236_9757
ER -
%0 Journal Article
%A Qinghou Zeng
%A Chunlei Zu
%T A generalization of Stiebitz-type results on graph decomposition
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9757/
%R 10.37236/9757
%F 10_37236_9757
Qinghou Zeng; Chunlei Zu. A generalization of Stiebitz-type results on graph decomposition. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9757
