Written on the Wall II - Conjecture 19 #
Reference: E. DeLaVina, Written on the Wall II, Conjectures of Graffiti.pc
theorem
WrittenOnTheWallII.GraphConjecture19.conjecture19
{α : Type u_1}
[Fintype α]
[DecidableEq α]
(G : SimpleGraph α)
[Nontrivial α]
(h_conn : G.Connected)
:
SimpleGraph.FLOOR (↑(∑ v : Set α, G.ecc v) / ↑(Fintype.card α) + sSup (Set.range G.indepNeighbors)) ≤ G.b
WOWII Conjecture 19
If G is connected then the size b(G) of a largest induced bipartite subgraph
satisfies
b(G) ≥ FLOOR((∑ ecc(v))/(|V|) + sSup (range (l G))), where ecc(v) denotes
eccentricity and l(G) is the independence number of neighbourhoods.