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PreprintCC BY 4.0arXiv

Code uniqueness of 4-cell connected disjoint clusters in spatial chromatic model

  • Weining Zhu
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Abstract

The spatial chromatic model (SCM) is a novel entity-oriented spatial data model proposed in recent years. Spatial tessellations formed by SCM have been applied in preliminary analyses of spatial point pattern recognition,spatial topology, and Voronoi diagram generation. Unlike previous spatial tessellation models, a key feature of SCM is that each subspace (cell) possesses a chromatic code, which serves as the foundation for various theoretical analyses and applications of SCM. The uniqueness of cell cluster codes in SCM constitutes an important property of the model. Previous studies have demonstrated the uniqueness of the chromatic codes of 2-cell and 3-cell connected disjoint clusters. Building on this analysis of connected cluster code characteristics, this paper proves the uniqueness of the chromatic codes of 4-cell connected disjoint clusters. The proof results and the new concepts introduced in this study help further refine the spatial chromatic model and provide a theoretical foundation for its subsequent applications.

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Cite

BibTeXRIS
BibTeX
@misc{zhu2026code,
  title = {{Code uniqueness of 4-cell connected disjoint clusters in spatial chromatic model}},
  author = {Weining Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37395},
  eprint = {2610.37395},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37395},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Code uniqueness of 4-cell connected disjoint clusters in spatial chromatic model
AU  - Weining Zhu
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37395
UR  - https://arxiv.org/abs/2610.37395
AB  - The spatial chromatic model (SCM) is a novel entity-oriented spatial data model proposed in recent years. Spatial tessellations formed by SCM have been applied in preliminary analyses of spatial point pattern recognition,spatial topology, and Voronoi diagram generation. Unlike previous spatial tessellation models, a key feature of SCM is that each subspace (cell) possesses a chromatic code, which serves as the foundation for various theoretical analyses and applications of SCM. The uniqueness of cell cluster codes in SCM constitutes an important property of the model. Previous studies have demonstrated the uniqueness of the chromatic codes of 2-cell and 3-cell connected disjoint clusters. Building on this analysis of connected cluster code characteristics, this paper proves the uniqueness of the chromatic codes of 4-cell connected disjoint clusters. The proof results and the new concepts introduced in this study help further refine the spatial chromatic model and provide a theoretical foundation for its subsequent applications.
ER  -