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adjacent algorithm array assume automorphism bipartite graph block graph block-spider blocking set chordal graphs Claim clique clique-Helly codes coloring column complete graph component computing Conjecture connected graph consider construct contains contradiction convex lattice Corollary defined denote diagonal digraph Discrete Math disjoint domatic number dominating set edges of G embedding exists Figure finite linear space geodetic cover geometry GIC set graph G Graph Theory green points Hamilton cycles Hence HS(n hypergraph induced subgraph interior hull interior lattice points interval graphs isomorphic labeling of type least Lemma Let G Levi graph log-concave lower bounds Mathematics matrix maximum genus minimal minimum ntype obtain partition path path-congruence perfect graphs permutation plane graph positive integer problem projective plane Proposition prove red points repeated blocks result sequence Steiner triple system subset supermagic Suppose tree unique upper embeddable vertex set vertices of G weight