Non-ambiguous trees: new results and generalisation (Full version)

如何在大型网络中应用树分解思想？

How to apply tree decomposition ideas in large networks?

针对树分解思想在大型网络中的应用问题，提出基于图分解的高效算法，经道路网络测试验证了其适用性，拓展了图分解的实际应用场景。

Guarded Second-Order Logic, Spanning Trees, and Network Flows

According to a theorem of Courcelle monadic second-order logic and guarded second-order logic (where one can also quantify over sets of edges) have the same expressive power over the class of all countable $k$-sparse hypergraphs. In the first part of the present paper we extend this result to hypergraphs of arbitrary cardinality. In the second part, we present a generalisation dealing with methods to encode sets of vertices by single vertices.