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assignment problem autotopism basis bipartite graph chiral chiral polytopes column Combinatorial complementing permutation complete bipartite graph Computer connected graph construct Corollary cube of order cycle defined defp degree sequence denote diagonal Latin squares dimension dimensionality edges edgesum equalized total Figure finite given graph G Graph Theory incidence vectors intersection interval graphs interval number interval representation ipath Iteration Latin squares left turn Lemma Let G level graph linear magic graph Mathematics matrix maximum minimum minimum-weight vectors nodes number of moves numbering of G obtained order q partition Petrie polygon Phase points polynomial Proof proper numbering puzzle recurrence Reed-Muller code regular polytope reliability s.c. graphs score sequences semifield plane sensitivity analysis shortest path simplex smallest solution algorithm square of order strongly diagonal Latin subgraph subnetwork sum deterministic tableau Theorem total chromatic total coloring Towers of Hanoi twisted field plane values Veronese map vertices weight