论文标题
从强烈规则的图表中，更多的两距离反示例概述了Borsuk的猜想
More two-distance counterexamples to Borsuk's conjecture from strongly regular graphs
论文作者
论文摘要
在2013年，Andriy V. Bondarenko展示了如何从任何强的定期图中构建两个距离的反例，其顶点集的任何强烈的定期图不是$ f+1 $ cliques（一组成对的相邻顶点）的结合，其中$ f $是其第二大eigenvalue Matixplicity的相互临近的多重性。 他将该构造应用于他能够证明的这两个图表：从$ g_2（4）$ graph（在416个顶点）中，他获得了65二维的两距离反例。从$ fi_ {23} $ graph（在31671顶点）中，他得到了一个782维的一个，并且通过考虑某些诱发子图，在Dimensions 781、780和779中进行了反例。 本文介绍了另外两个强烈的规则图，可在28431和2401（分别为2401）的顶点。它给出了从781的尺寸，从较大图衍生的764个维度（事实证明是$ fi_ {23} $ graph）和一个240维的反例。 几个包含的命题依赖于（通常是广泛）计算的结果，主要是在计算机代数系统间隙内。源软件包包含（几乎）所有使用的源文件。
In 2013 Andriy V. Bondarenko showed how to construct a two-distance counterexample to Borsuk's conjecture from any strongly regular graph whose vertex set is not the union of at most $f+1$ cliques (sets of pairwise adjacent vertices) where $f$ is the multiplicity of the second-largest eigenvalue of its adjacency matrix. He applied that construction to those two graphs that he had been able to prove to fulfill the condition: From the $G_2(4)$ graph (on 416 vertices) he got a 65-dimensional two-distance counterexample. From the $Fi_{23}$ graph (on 31671 vertices) he got a 782-dimensional one and, by considering certain induced subgraphs, counterexamples in dimensions 781, 780 and 779. This article presents two other strongly regular graphs fulfilling the condition, on 28431 and on 2401, resp., vertices. It gives dedicated counterexamples in dimensions from 781 down to 764 derived from the bigger graph (that turned out to be an induced subgraph of the $Fi_{23}$ graph) and a 240-dimensional counterexample derived from the smaller graph. Several contained propositions rely on the results of (often extensive) computations, mainly within the computer algebra system GAP. The source package contains (almost) all used source files.
