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math.CO2026
There is no -regular -irregular graph
Artem Hak, Sergiy Kozerenko, Andrii Serdiuk
A graph is -irregular if its vertices belong to pairwise distinct numbers of triangles. We prove that no -regular -irregular graph exists, settling the last unresolved…
math.CO2026
Regular -regular graphs
Artem Hak, Sergiy Kozerenko, Denys Lohvynov +1
We study graphs that are simultaneously regular with respect to the ordinary vertex degree and regular with respect to the triangle degree, that is, the number of triangles contain…