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Knights Tours and Magic Squares by Barry A Balof and John J WatHns
Decompositions of the Complete Digraph into each of the Orientations
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1-closed labeling 3-connected 4-clique a+c+d adjacent assume binary binary trees bipartite graph cc(G chordal graphs chromatic polynomial complete graph components computation contains contradiction Corollary corresponding cutset cycle D(RJ defined degree deletion denote diagonal diameter disjoint paths dominating set domination number elements equation exists Figure G E(G graph G graph of order Graph Theory Halin graphs Hamiltonian Hence Hilbert function implies incidence matrix induced subgraphs induction intersection interval graph isomorphic LC graphs learning algorithm least Lemma length Let G linear matching Math Mathematics matroid maximum median minimally triangle-saturated modular threshold graph neutral edge nodes NP-complete number of edges obtained optimal orientation pair partition permutation positive integer Principle problem Proof Proposition result robots series-parallel network starred copair Steiner subgraph subset Suppose Theorem threshold graphs tree variables vertex vertex of G vertices visibility graph Xj(v