Abstract: In this paper, Heawood's counterexample graph is artificially colored by using the algorithm of planar graph four-colorable based on path homotopy search, which verifies the feasibility and ...

While retrieval-augmented generation is effective for simpler queries, advanced reasoning questions require deeper connections between information that exist across documents. They require a knowledge ...

#define _(blk) std::cerr << #blk << " "; start_ = clock(); blk \ std::cerr << (clock()-start_)*1.0/CLOCKS_PER_SEC << "s" << std::endl; "simple_maximal_planar_random ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Fuzzy modeling plays a pivotal role in various fields, including science, engineering, and medicine. In comparison to conventional models, fuzzy models offer enhanced accuracy, adaptability, and ...

Abstract: Graph partitioning is an essential preprocessing step in distributed graph computation and scientific simulations. Existing well-studied graph partitioners are designed for static graphs, ...

Given a planar, undirected, graph enumerate all of the faces of the graph. Can also be described as finding all of the polygons within the graph, or the minimum cycle basis, based on Geometric Tools ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...