图的无爪性、3-齐次子集与一个重构问题
Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem
摘要：
我们描述了图类$Forb\{K_{1,3}, \overline {K_{1,3}}\}$，使得$G$及其补图$ \overline{G}$是无爪的。除了少数例外，它是由图的连通组成部分包括长度至少为4的圈，路径或孤立顶点，以及这些图的补图。考虑由图$G$的顶点集的3元子集构成的超图${\mathcal H} ^{(3)}(G)$，$G$在其上导出一个团或一个独立子集，我们由此推出两个图$G$和$G'$的布尔和$G\dot{+}G'$的描述，给出同一超图.我们表明后一种描述的作用，在重建问题的图形互补。
英文摘要：
We describe $Forb\{K_{1,3}, \overline {K_{1,3}}\}$, the class of graphs $G$ such that $G$ and its complement $ \overline{G}$ are claw-free. With few exceptions, it is made of graphs whose connected components consist of cycles of length at least 4, paths or isolated vertices, and of the complements of these graphs. Considering the hypergraph ${\mathcal H} ^{(3)}(G)$ made of the 3-element subsets of the vertex set of a graph $G$ on which $G$ induces a clique or an independent subset, we deduce from above a description of the Boolean sum $G\dot{+}G'$ of two graphs $G$ and $G'$ giving the same hypergraph. We indicate the role of this latter description in a reconstruction problem of graphs up to complementation.
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。
