This work considers new entropy-based proofs of some known, or otherwise refined, combinatorial bounds for bipartite graphs. These include upper bounds on the number of the independent sets, lower bounds on the minimal number of colors in constrained edge coloring, and lower bounds on the number of walks of a given length in bipartite graphs. The proofs of these combinatorial results rely on basic properties of the Shannon entropy.

翻译：这项工作将考虑一些已知或以其他方式改进的双边图形组合框的新的基于星盘的新型证据。 其中包括独立集数的上限、 限制边缘颜色中最低颜色数的下限、 以及双边图形中特定长度行道数的下限。 这些组合结果的证明依赖于香农 entropy 的基本特性 。