References & Citations
Mathematics > Combinatorics
Title: Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurations
(Submitted on 14 Aug 2022 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: 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.
Submission history
From: Benjamin Peet [view email][v1] Sun, 14 Aug 2022 20:41:44 GMT (15106kb,D)
[v2] Fri, 26 Apr 2024 16:45:59 GMT (1232kb,D)
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