论文标题
Ramsey数字和最小单色三角形数量的变化$ 2 $ - 颜色的配置
Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurations
论文作者
论文摘要
本文首先探讨了一些有关拉姆齐数字和最小数量的单色三角形数量的新旧结果，其中包括$ 2 $ - 完整图的颜色，无论是在脱节和非偶发外案例中。然后，我们通过定义点和线的配置的线条$ 2 $颜色来扩展理论，并考虑最少数量的非分离单色三角形数量。我们在考虑通过入射开关的添加或连接配置之和的一般结果之前，为著名的对称$ v_ {3} $配置计算特定示例。纸张通过考虑最大数量的相互交叉线的数量来完成，以及这与给定的三角形的最小数量$ 2 $ 2 $ - 颜色对称$ v_ {3} $配置。
This paper begins by exploring some old and new results about Ramsey numbers and minimum numbers of monochromatic triangles in $2$-colorings of complete graphs, both in the disjoint and non-disjoint cases. We then extend the theory, by defining line $2$-colorings of configurations of points and lines and considering the minimum number of non-disjoint monochromatic triangles. We compute specific examples for notable symmetric $v_{3}$ configurations before considering a general result regarding the addition or connected sum of configurations through incidence switches. The paper finishes by considering the maximal number of mutually intersecting lines and how this relates to the minimum number of triangles given a line $2$-coloring of a symmetric $v_{3}$ configuration.
