论文标题
极端图，用于悬挂边缘临界图
Extremal graphs for the suspension of edge-critical graphs
论文作者
论文摘要
图形$ h $，$ \ text {ex}（n，h）$的图片是$ n $ vertex图中不包含$ h $作为子图的最大边数。对于一个顶点$ v $和图形的多集$ \ Mathcal {f} $，悬架$ \ MATHCAL {F}+V $ $ \ MATHCAL {F} $是通过将pertex $ v $连接到每个$ f $ f \ in \ nath \ nath \ nath \ nath \ nation \ f}的$ f $ of $ f $的图形。对于两个整数$ k \ ge1 $和$ r \ ge2 $，让$ h_i $为一个图表，包含一个关键边缘，具有任何$ i \ in \ in \ {1，\ ldots，k \} $，然后让$ h = \ h = \ {在本文中，我们确定$ \ text {ex}（n，h）$，并表征所有极大的$ n $的极端图。这概括了Chen，Gould，Pfender和WEI在相交集团上的结果。我们还获得了$ H $的稳定定理，这是Roberts和Scott在包含关键边缘的图表上的结果。
The Turán number of a graph $H$, $\text{ex}(n,H)$, is the maximum number of edges in an $n$-vertex graph that does not contain $H$ as a subgraph. For a vertex $v$ and a multi-set $\mathcal{F}$ of graphs, the suspension $\mathcal{F}+v$ of $\mathcal{F}$ is the graph obtained by connecting the vertex $v$ to all vertices of $F$ for each $F\in \mathcal{F}$. For two integers $k\ge1$ and $r\ge2$, let $H_i$ be a graph containing a critical edge with chromatic number $r$ for any $i\in\{1,\ldots,k\}$, and let $H=\{H_1,\ldots,H_k\}+v$. In this paper, we determine $\text{ex}(n, H)$ and characterize all the extremal graphs for sufficiently large $n$. This generalizes a result of Chen, Gould, Pfender and Wei on intersecting cliques. We also obtain a stability theorem for $H$, extending a result of Roberts and Scott on graphs containing a critical edge.
