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A new bound for the 2/3 conjecture

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Figure

Figure 1: The elements of F3. The edges of color 1, 2 and 3 are represented by solid,dashed and dotted lines, respectively.
Figure 2: The elements σ1, . . . , σ7 of F4. The edges of color 1, 2 and 3 are represented bysolid, dashed and dotted lines, respectively.
Table 1: The values εc(σi) for i ∈ {1, . . ., 7} and c ∈ {1, 2, 3}.
Table 2 (in Appendix B). In addition, (2) ensures that qG(H) is also non-negative for eachelement H of A corresponding to any of the first four columns of Table 3 (in Appendix B).Note that these elements can be expressed as elements of R
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