论文标题
奇数和最小程度较大的图表上的过时猜想
The overfull conjecture on graphs of odd order and large minimum degree
论文作者
论文摘要
令$ g $为最大程度$δ（g）$的简单图。如果$ | e（h）|>δ（g）\ lfloor \ frac {1} {2} {2} | v（h）| \ rfloor $。 Chetwynd和Hilton在1986年猜想，$δ（g）> \ frac {1} {3} {3} | v（g）| $具有彩色索引$δ（g）$，并且仅当$ g $包含Overfull overfull sub graph。令$ 0 <\ varepsilon <1 $和$ g $为$ n $顶点的大图，至少$ \ frac {1} {2} {2}（1+ \ varepsilon）n $。结果表明，如果$ n $甚至是$ n $，则猜想的价格为$ g $。在本文中，如果$ n $奇怪，则证明了相同的结果。据我们所知，这是构造奇数顺序图和最小程度约束的猜想的第一个结果。
Let $G$ be a simple graph with maximum degree $Δ(G)$. A subgraph $H$ of $G$ is overfull if $|E(H)|>Δ(G)\lfloor \frac{1}{2}|V(H)| \rfloor$. Chetwynd and Hilton in 1986 conjectured that a graph $G$ with $Δ(G)>\frac{1}{3}|V(G)|$ has chromatic index $Δ(G)$ if and only if $G$ contains no overfull subgraph. Let $0<\varepsilon <1$ and $G$ be a large graph on $n$ vertices with minimum degree at least $\frac{1}{2}(1+\varepsilon)n$. It was shown that the conjecture holds for $G$ if $n$ is even. In this paper, the same result is proved if $n$ is odd. As far as we know, this is the first result on the conjecture for graphs of odd order and with a minimum degree constraint.
