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.