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The evolution of unavoidable bi-chromatic patterns and extremal cases of balanceability
[article]
2022
arXiv
pre-print
We study the color patterns that, for n sufficiently large, are unavoidable in 2-colorings of the edges of a complete graph K_n with respect to min{e(R), e(B)}, where e(R) and e(B) are the numbers of red and, respectively, blue edges. More precisely, we determine how such unavoidable patterns evolve from the case without restriction in the coloring, namely that min{e(R), e(B)}≥ 0 (given by Ramsey's theorem), to the highest possible restriction, namely that |e(R) - e(B)| ≤ 1. We also investigate
arXiv:2204.04269v1
fatcat:vhin3gldsvb7zcbjobgsesye74