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pro vyhledávání: '"Higgins, Cecelia"'
Autor:
Grebík, Jan, Higgins, Cecelia
We show that the set of locally finite Borel graphs with finite Borel asymptotic dimension is $\mathbf{\Sigma}^1_2$-complete. The result is based on a combinatorial characterization of finite Borel asymptotic dimension for graphs generated by a singl
Externí odkaz:
http://arxiv.org/abs/2411.08797
Autor:
Higgins, Cecelia
We prove a descriptive version of Brooks's theorem for directed graphs. In particular, we show that, if $D$ is a Borel directed graph on a standard Borel space $X$ such that the maximum degree of each vertex is at most $d \geq 3$, then unless $D$ con
Externí odkaz:
http://arxiv.org/abs/2405.00991