Minor of graph:
deletion of edges and/or vertices; and contraction of edges to vertices
deletion of edges and/or vertices; and contraction of edges to vertices
Looking at families of graphs that are closed under taking minors [i.e. coarse-graining]
E.g. planarity
Examples:
Apex graph
Toroidal graph
Graphs that can be embedded on any fixed 2D manifold
Graphs of any fixed genus
For any family closed under minor taking, there is a finite set of forbidden minors
E.g. planarity
Examples:
Apex graph
Toroidal graph
Graphs that can be embedded on any fixed 2D manifold
Graphs of any fixed genus
For any family closed under minor taking, there is a finite set of forbidden minors
Conservation of genus under graph minoring....
If you can’t generate a forbidden minor, you stay e.g. in the genus
[[ In a first approximation, every forbidden minor corresponds to a particle ]]
If you can’t generate a forbidden minor, you stay e.g. in the genus
[[ In a first approximation, every forbidden minor corresponds to a particle ]]
https://en.wikipedia.org/wiki/Forbidden_graph_characterization
https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theorem
“Finite obstruction set for each genus”
https://mathoverflow.net/questions/46655/obstructions-for-embedding-a-graph-on-a-surface-of-genus-g
https://arxiv.org/pdf/1608.04066.pdf