论文标题
外平面3-均匀超图的最大光谱半径
Maximum spectral radius of outerplanar 3-uniform hypergraphs
论文作者
论文摘要
在本文中，我们研究了外平面的最大光谱半径$ 3 $均匀的超图。给定$ \ Mathcal {h} $的阴影是一个图形$ g $，带有$ v（g）= V（\ Mathcal {h}）$和$ e（g）= \ {uv {uv：uv：uv in h \ textrm {如果可以将图形嵌入到平面中，以使其所有顶点都位于外部面上，则图形为\ textit {ofterplanar}。如果$ 3 $ - 均匀的超图$ \ MATHCAL {H} $称为\ Textit {ofterPlanar}，如果其阴影的阴影具有外平面嵌入，以致$ \ Mathcal {h h} $的每个超edge是阴影的内部三角形面的顶点。 Cvetković和Rowlinson在1990年猜想，在$ n $顶点的所有外部平面图中，图$ k_1+ p_ {n-1} $达到了最大光谱半径。我们显示了Cvetković-Rowlinson猜想的超图类似物。特别是，我们表明，对于足够大的$ n $，$ n $ vertex ofterplanar $ 3 $均匀的最大光谱半径是唯一的$ 3 $ - $ 3 $ - 均匀的超刻画，其阴影为$ k_1 + p_1 + p_ {n-1} $。
In this paper, we study the maximum spectral radius of outerplanar $3$-uniform hypergraphs. Given a hypergraph $\mathcal{H}$, the shadow of $\mathcal{H}$ is a graph $G$ with $V(G)= V(\mathcal{H})$ and $E(G) = \{uv: uv \in h \textrm{ for some } h\in E(\mathcal{H})\}$. A graph is \textit{outerplanar} if it can be embedded in the plane such that all its vertices lie on the outer face. A $3$-uniform hypergraph $\mathcal{H}$ is called \textit{outerplanar} if its shadow has an outerplanar embedding such that every hyperedge of $\mathcal{H}$ is the vertex set of an interior triangular face of the shadow. Cvetković and Rowlinson conjectured in 1990 that among all outerplanar graphs on $n$ vertices, the graph $K_1+ P_{n-1}$ attains the maximum spectral radius. We show a hypergraph analogue of the Cvetković-Rowlinson conjecture. In particular, we show that for sufficiently large $n$, the $n$-vertex outerplanar $3$-uniform hypergraph of maximum spectral radius is the unique $3$-uniform hypergraph whose shadow is $K_1 + P_{n-1}$.
