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math.CO2026
New mixed cages, bounds and computational results
Claudia Marlene De la Cruz, Miguel Ángel Pizaña
An -mixed cage is a mixed graph that is -regular in edges, -regular in arcs, of girth and of minimum order . We give a general lower bound for $n(r,z…
math.CO2026
There are no nontrivial chordal square-complementary graphs
Pierre Aboulker, Martin Milanič, Peter Muršič +1
We study square-complementary graphs (satisfying ). We show that in such graphs, no two vertices have comparable closed neighborhoods. This implies that…