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2-coloring impartial game on some regular and semiregular polyhedron graphs |
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| รหัสดีโอไอ | |
| Title | 2-coloring impartial game on some regular and semiregular polyhedron graphs |
| Creator | Boonyarit Boon-im |
| Contributor | Borworn Khuhirun, Advisor |
| Publisher | Thammasat University |
| Publication Year | 2568 |
| Keyword | Regular polyhedron, Platonic solid, Archimedean solid, Coloring game, Graph |
| Abstract | We study a 2-coloring impartial game on graphs, called a vertex coloring game, where two players alternately color vertices using two colors while avoiding coloring adjacent vertices with the same color. An edge-coloring game in which the analogous rules apply is also investigated. We prove that the second player has a winning strategy in vertex-coloring games on Platonic solid graphs and Archimedean solid graphs, as well as, in edge-coloring games on Platonic solid graphs. Computational techniques are implemented in Python to verify the winning strategies on small cases. |
