Icosian Game

Author

Eric W. Weisstein
November 9, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/IcosianGame.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/IcosianGame.html.

©2023 Wolfram Research, Inc. except for portions noted otherwise

Solutions

With[{gn="DodecahedralGraph"},With[{hc=FindHamiltonianCycle[GraphData[gn],All][[All,All,1]]},GraphicsGrid[Partition[HighlightGraph[Annotate[GraphData[gn],EdgeStyle->Gray],Style[UndirectedEdge@@@Partition[#,2,1,1],Directive[Thick,Red]]]&/@hc,UpTo[6]],ImageSize->700]]]

Multiway deletions graph

https://writings.stephenwolfram.com/2022/06/games-and-puzzles-as-multicomputational-systems/#the-icosian-game-&-some-relatives

({{"[◼]", "StyledDeletionsGraph" }})[({{"[◼]", "MultiwayDeletionsGraph" }})[
GraphData["DodecahedralGraph"],{1},VertexDelete,3],
GraphData["DodecahedralGraph"],VertexSize->1.3,"InnerVertexSize"->1.1,
GraphLayout->"LayeredDigraphEmbedding",PerformanceGoal->"Quality",ImageSize->700]