论文标题
具有最小核心程度的边缘临界图的过度
Overfullness of edge-critical graphs with small minimal core degree
论文作者
论文摘要
令$ g $为一个简单的图表。用$ n $，$δ（g）$和$χ'（g）$表示为订单，最高学位和$ g $的色度指数。我们称$ g $ 如果$ | e（g）|/\ lfloor n/2 \ rfloor>δ（g）$，而{\ it Crigith}如果$χ'（h）<χ'（g）$ for $ g $ g $ $ h $ of $ g $。显然，如果$ g $被覆盖，则$χ'（g）=δ（g）+1 $。 $ g $的\ emph {core}，用$g_δ$表示，是其所有最高度顶点引起的$ g $的子图。我们认为，利用核心学位条件可以被视为攻击过度猜想的一种方法。沿着这个方向，我们在本文中表明，对于任何整数$ k \ geq 2 $，如果$ g $对于$δ（g）\ geq \ frac {2} {2} {3} n+\ frac {3k} {3k} {2} {2} {2} {2} $ up $δ（g_Δ）\ leq k $，那么$ g $的$ G $是$ G $。
Let $G$ be a simple graph. Denote by $n$, $Δ(G)$ and $χ' (G)$ be the order, the maximum degree and the chromatic index of $G$, respectively. We call $G$ \emph{overfull} if $|E(G)|/\lfloor n/2\rfloor > Δ(G)$, and {\it critical} if $χ'(H) < χ'(G)$ for every proper subgraph $H$ of $G$. Clearly, if $G$ is overfull then $χ'(G) = Δ(G)+1$. The \emph{core} of $G$, denoted by $G_Δ$, is the subgraph of $G$ induced by all its maximum degree vertices. We believe that utilizing the core degree condition could be considered as an approach to attacking the overfull conjecture. Along this direction, we in this paper show that for any integer $k\geq 2$, if $G$ is critical with $Δ(G)\geq \frac{2}{3}n+\frac{3k}{2}$ and $δ(G_Δ)\leq k$, then $G$ is overfull.
