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Coloring powers of random graphs

math.CO · 2026-04-15 · unverdicted · novelty 7.0

For p = d/n the r-th power has maximum degree ~ log n over (r+1)-fold log and chromatic number sandwiched between the maximum degrees of the floor(r/2) and (r-1) powers plus one (equality at r=2); for d = omega(log n) up to n^{1/r-Omega(1)} the chromatic number is Theta(d^r / log d).

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  • Coloring powers of random graphs math.CO · 2026-04-15 · unverdicted · none · ref 4

    For p = d/n the r-th power has maximum degree ~ log n over (r+1)-fold log and chromatic number sandwiched between the maximum degrees of the floor(r/2) and (r-1) powers plus one (equality at r=2); for d = omega(log n) up to n^{1/r-Omega(1)} the chromatic number is Theta(d^r / log d).