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adjacent algorithm Amer array BIBD block Canad cardinality cells characterization clique CM CM CM co-circuit Combinatorial conjecture connected matroid construction contains Corollary cycle d-arrangement defined deleting denote diagonal steps disjoint distinct eigenvalues equations equivalence class exists Figure finite G and H given graph G Graph Theory H is flexible Harary Hence induction integer isomorphic isomorphic to H left-decap Lemma Let G Let H line graph line isomorphisms loops M-circuit Math matrix minimally 2-connected graphs minimally strong digraphs obtained odd degreed pair pairwise balanced design partition planar planar graph plane points positive integers prime problem Proof Proposition prove pseudographs RBPD Room square Schur theorem simple path insertion solution Steiner triple systems subarray subgraph subset Suppose symbols symmetric symmetric difference Theorem triple systems University of Manitoba University of Waterloo valency values vertex vertices W. T. Tutte weighted lattice paths zonotopes