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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Benjamin Peet
St. Martin's University, Lacey WA, USA
Electrical & Electronics Engineering

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Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurations Jamie Bishop; Rebekah Kuss; Benjamin Peet
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.8

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 v3 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 v3 configuration.
Co-Authors Jamie Bishop Rebekah Kuss