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2-colorable 4TH S-E CONF abelian group adjacent algorithm array of order balanced incomplete block Baumert-Hall array bicritical binary bipartite graph block design boundary colorations braid chain-group circuit Combinatorial Theory conjecture consider construction contains core cycle defined definition denote digits edges equation example exist finite four coloring given graph G Graph Theory Hadamard matrices hamiltonian Hamiltonian graphs hence hypergraph incidence geometry incidence matrix incomplete block design integer isomorphic Jennifer Seberry k-tuples labeled Lemma Let G lower bound Math matroid maximal snakes minimal n-set nodes obtained occurs pair parameters partially ordered partially ordered set partition perfect 1-factorization permutation groups planar graph polynomial prime power problem PROC projective plane Proof reduced sequences Room square satisfy skew Stanton starter subcube subset Suppose symmetric snake T-sequence Table tactical configurations Theorem tree Turyn upper bound values vertices wreath