稠密欧拉图是$(1, 3)$ -可选图
Dense Eulerian graphs are $(1, 3)$-choosable
摘要：
图$G$是总权重$(k,k')$ -可选择的，如果对于向每个顶点$v$分配$k$实数的集合$L(v)$并且向每个边$e$分配$k'$实数的集合$L(e)$的任何总列表分配$L$，存在适当的总$L$ -加权，即，- 映射$f: V(G) \cup E(G) \to \mathbb{R}$，使得对于每个$z \in V(G) \cup E(G)$，$f(z) \in L(z)$，并且对于$G$的每个边$uv$，$\sum_{e \in E(u)}f(e)+f(u) \ne \sum_{e \in E(v)}f(e) + f(v)$。本文证明了若$G$分解为奇数阶完全图，则$G$是全权$(1,3)$ -可选的.因此，每一个最小度至少为$0.91|V(G)|$的高阶欧拉图$G$都是全权$(1,3)$ -可选择的.证明了最小度至少为$0.999|V(G)|$的图$G$是全权$(1,4)$ -可选的.
英文摘要：
A graph $G$ is total weight $(k,k')$-choosable if for any total list assignment $L$ which assigns to each vertex $v$ a set $L(v)$ of $k$ real numbers, and each edge $e$ a set $L(e)$ of $k'$ real numbers, there is a proper total $L$-weighting, i.e., a mapping $f: V(G) \cup E(G) \to \mathbb{R}$ such that for each $z \in V(G) \cup E(G)$, $f(z) \in L(z)$, and for each edge $uv$ of $G$, $\sum_{e \in E(u)}f(e)+f(u) \ne \sum_{e \in E(v)}f(e) + f(v)$. This paper proves that if $G$ decomposes into complete graphs of odd order, then $G$ is total weight $(1,3)$-choosable. As a consequence, every Eulerian graph $G$ of large order and with minimum degree at least $0.91|V(G)|$ is total weight $(1,3)$-choosable. We also prove that any graph $G$ with minimum degree at least $0.999|V(G)|$ is total weight $(1,4)$-choosable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
