Documentation

HexGraphIso.Nauty.Sparse.VertexKey

def Hex.GraphIso.Nauty.Sparse.vertexKey {n : Nat} (G : SparseGraph n) (tcLevel fuel level : Nat) (lab ptn : Array Nat) (tc numcells v : Nat) :
Key n

The unpruned sparse child maximum indexed by its literal chosen vertex.

Equations
  • One or more equations did not get rendered due to their size.
Instances For
    theorem Hex.GraphIso.Nauty.Sparse.Ready.window_target {n k : Nat} {G : Sparse.Colored n k} {level numcells tc len : Nat} {st : State n} (_h : Ready G level numcells st) (hc : IsCell st.ptn level tc len) (hlen : 1 < len) (hr : tc + len ≤ n) :
    Generic.Target State.frame level tc (windowSet n st.lab tc len) st

    A full parent cell is a valid target for each of its native children.

    theorem Hex.GraphIso.Nauty.Sparse.Ready.vertex_key {n k : Nat} {G : Sparse.Colored n k} {level numcells tc len v fuel : Nat} {st : State n} {gamma : Array Nat} (h : Ready G level numcells st) (hn : 0 < n) (hl : 1 ≤ level) (ha : checkAutom (Graph.context G.graph).g gamma = true) (hstab : CellStab st.ptn level st.lab gamma) (hc : IsCell st.ptn level tc len) (hlen : 1 < len) (hr : tc + len ≤ n) (hv : (windowSet n st.lab tc len).mem v = true) (hf : n < fuel + (numcells + 1)) (tcLevel : Nat) :
    vertexKey G.graph tcLevel fuel level st.lab st.ptn tc numcells v = vertexKey G.graph tcLevel fuel level st.lab st.ptn tc numcells gamma[v]!

    A checked automorphism stabilizing the current cells identifies the entire native child maxima at the vertices it carries. The proof transports every unpruned leaf through the actual individualization and sparse dispatch.