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The Game Chromatic Number of Complete Multipartite Graphs with Singletons and Large Parts

Abstract

We study the game chromatic number of complete multipartite graphs whose parts are either singletons or are of size at least four. Building on the work of PawełObszarski et al., we give a formula in terms of the ordered part sizes, and the number of singleton parts.

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BibTeX
@misc{jayasinghe2026game,
  title = {{The Game Chromatic Number of Complete Multipartite Graphs with Singletons and Large Parts}},
  author = {Lasitha Jayasinghe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12508},
  eprint = {2610.12508},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12508},
}
RIS
TY  - UNPB
TI  - The Game Chromatic Number of Complete Multipartite Graphs with Singletons and Large Parts
AU  - Lasitha Jayasinghe
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.12508
UR  - https://arxiv.org/abs/2610.12508
AB  - We study the game chromatic number of complete multipartite graphs whose parts are either singletons or are of size at least four. Building on the work of PawełObszarski et al., we give a formula in terms of the ordered part sizes, and the number of singleton parts.
ER  -