This two-volume set, LNCS 15983 and 15984 , constitutes the referred proceedings of the 31st International Computing and Combinatorics Conference, COCOON 2025, held in Chengdu, China, during August 15&17, 2025. The 54 full papers were carefully reviewed and selected from 191 submissions. COCOON 2025 provided an excellent venue for researchers working in the topical sections as follows: Part I: Approximation Algorithms, Combinatorial Optimization, Computational Complexity, Computational Geometry, Economics and Computation. Part II: Graph Algorithms and Graph Theory, Learning and Data-Related Theory, Parameterized Algorithms, String Algorithms and Discrete Structures.