Making A K4-free Graph Bipartite
Mathematics Project Topics
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This paper presents every K4-free graph G with n vertices can be madernbipartite by deleting at most n2rn9 edges. Moreover, the only extremal graphrnwhich requires deletion of that many edges is a complete 3-partite graph withrnparts of size n=3
Subsurface Intelligence & Critical Mineral Exploration
Modern Geology projects now focus on Machine Learning in Mineral Targeting, Carbon Capture & Storage (CCS) Geologic Modeling, and Critical Mineral Systems (Lithium, REEs). If your research involves Hydrogeological Connectivity, Seismic Inversion, or Geotechnical Site Characterization, ensure your analysis follows the JORC or NI 43-101 reporting standards and utilizes robust 3D Subsurface Visualization and Geochemical Fingerprinting frameworks.
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