Timeline for Name of a game : Remove two chips from a vertex or one chip from both ends of an edge
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2021 at 13:31 | answer | added | Timothy Chow | timeline score: 4 | |
| Oct 17, 2021 at 23:32 | comment | added | Richard Stanley | The case of a path with each $n_v=1$ is equivalent to Dawson's Kayles. I believe this game was first analyzed by Guy and Smith, The $G$-values for various games, Proc. Cambridge Phil. Soc. 52 (1956), 514-526. | |
| Oct 17, 2021 at 20:00 | comment | added | Roland Bacher | @RichardStanley I have a slight preference for a formulation without loops : It has a straightforward generalization to simplicial complexes having simplices of dimension at most $d$ : Chose a simplex of dimension $k$ and remove from its $k+1$ vertices $(d+1)!/(k+1)$ chips (if possible). I guess the one-dimensional case of graphs is already quite complicated. | |
| Oct 17, 2021 at 18:27 | history | edited | YCor | CC BY-SA 4.0 |
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| Oct 17, 2021 at 14:16 | comment | added | Richard Stanley | More generally, we can allow $\Gamma$ to have loops (edges from a vertex to itself), regarded as having two endpoints. Now the only rule is that we can remove one chip from both endpoints of an edge if the number of chips remains nonnegative at each vertex. | |
| Oct 17, 2021 at 9:57 | history | asked | Roland Bacher | CC BY-SA 4.0 |