AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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A quasi-tree of a connected ribbon graph is a spanning ribbon subgraph with exactly one boundary component; quasi-trees play the role of spanning trees in the topological graph theory of embedded graphs. We prove that counting them is #P-complete under polynomial-time Turing reductions, already for bouquets. The proof...
We prove a conjecture of Regts and Sevenster: a complex-valued graph parameter $f$ with $f(\varnothing)=1$ has exponentially bounded edge-connection rank if and only if it is a mixed partition function; moreover, the model may be chosen with its numbers of even and odd colours explicitly bounded in terms of the rank bo...
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