For every d >= 3 and n = k d with k >= 2, there exist directed d-regular graphs on n vertices whose random cycle-factors have expected cycle count strictly larger than k H_d, disproving the conjecture that the disjoint union of K_d^circ maximizes it.
On the path partition number of 6-regular graphs.J
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Counterexamples to an Extremal Conjecture for Random Cycle-Factors
For every d >= 3 and n = k d with k >= 2, there exist directed d-regular graphs on n vertices whose random cycle-factors have expected cycle count strictly larger than k H_d, disproving the conjecture that the disjoint union of K_d^circ maximizes it.