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arXiv 1908.06656cs.DM
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关于边双点图和迭代边双点算子

On the edge-biclique graph and the iterated edge-biclique operator

Leandro Montero, Sylvain Legay

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摘要：

图$G$的一个双团是图$G$的一个极大导出完全二部子图。$G$的边二分图$KB_e(G)$是$G$的二分图的边交图。图$G$发散（分别收敛或者是周期性的），无论何时$H$（或对于某些$m$为$\lim_{k \rightarrow \infty}H^k(G)=H^m(G)$，对于某些$k$和$s \geq 2$为$H^k(G)=H^{k+s}(G)$）。$G$的迭代边偶图$KB_e^k(G)$是通过将边偶算子$k$连续多次应用于$G$而得到的图。本文首先研究了$G$和$KB_e(G)$之间的连通关系。其次，我们研究了迭代边双团算子$KB_e$。特别地，我们给出了一个图在算子$KB_e$下收敛或发散的充分条件，刻画了\textit{burgeon graphs}的行为，并给出了一些一般性的结论.

英文摘要：

A biclique of a graph $G$ is a maximal induced complete bipartite subgraph of $G$. The edge-biclique graph of $G$, $KB_e(G)$, is the edge-intersection graph of the bicliques of $G$. A graph $G$ diverges (resp. converges or is periodic) under an operator $H$ whenever $\lim_{k \rightarrow \infty}|V(H^k(G))|=\infty$ (resp. $\lim_{k \rightarrow \infty}H^k(G)=H^m(G)$ for some $m$ or $H^k(G)=H^{k+s}(G)$ for some $k$ and $s \geq 2$). The iterated edge-biclique graph of $G$, $KB_e^k(G)$, is the graph obtained by applying the edge-biclique operator $k$ successive times to $G$. In this paper, we first study the connectivity relation between $G$ and $KB_e(G)$. Next, we study the iterated edge-biclique operator $KB_e$. In particular, we give sufficient conditions for a graph to be convergent or divergent under the operator $KB_e$, we characterize the behavior of \textit{burgeon graphs} and we propose some general conjectures on the subject.

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。

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