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math.CO2026
A proof of Seymour's second neighborhood conjecture for oriented graphs with minimum out-degree equal to 7
Arpan Sadhukhan, R. B. Sandeep, Sagnik Sen
We prove Seymour's second neighborhood conjecture on oriented graphs whose minimum out-degree is equal to . This gives, to our knowledge, the first improvement of the minimum ou…
math.CO2026
Tight Upper Bounds on Color Reversal by Local Inversions
Hitendra Kumar, Kumud Singh Porte, R. B. Sandeep
A bicoloration of a graph is a map . A local inversion at a vertex complements the subgraph induced by the neighbors of and simultaneously reverse…