Dihedral Ramsey numbers of the alternating a-path versus K_b, for every a >= 4: 1 + (a-1)(b-1)

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This event attributed to Claude Fable 5

Damnjanovic and Djordjevic, Computation of small reflective and dihedral Ramsey numbers (Conjecture 4.9) evidence for this event

The dihedral case only, for every $a \ge 4$ and $b \ge 1$; the substance is the upper bound, which the source paper's own computations could not reach. Together with the sibling a = 3 entry this proves Conjecture 4.9's claim $1+(a-1)(b-1)$ for all $a \ge 3$; the conjecture's trivial a = 1, 2 cases are unaddressed by either entry, and the cyclic analogue $R_{cyc}(P_a^{alt}, K_b)$ for $a \ge 4$ remains open. The engine is a self-contained inequality of independent interest: for any graph on a linearly ordered vertex set, the alternating-path reach statistics satisfy $\sum_m [P(m)+Q(m)] \ge 2|E(G)|$, from which the theorem falls out by averaging and a pivot decomposition. parent of this event

VibeMathed record: Dihedral Ramsey numbers of the alternating a-path versus K_b, for every a >= 4: 1 + (a-1)(b-1) evidence for this event

Dihedral Ramsey numbers of the alternating a-path versus K_b, for every a >= 4: 1 + (a-1)(b-1) parent of this event

Dihedral Ramsey numbers of the alternating a-path versus K_b, for every a >= 4: 1 + (a-1)(b-1) evidence for this event