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1-factorization 5TH S-E CONF adjacency matrix algorithm automorphism balanced design bound chromatic number circuit clique coloring column COMBINATORICS complete COMPUTING connected graph consider construction contains coordinate Corollary corresponding cosets cubic graph cycle defined degree denote digraph disjoint edges elements exactly example exists finite functions given graph G GRAPH THEORY Hamiltonian Hence homeomorphic independence graphs independent set induced integer intersection graph interval graph isomorphic Latin square Lemma length Let G Math matroid maximum minimum forest n-coloring n-tuple nodes number of vertices obtained optional points orbit pair palindrome parameters partition path permutation planar plane graph points of G polynomial algorithm positive integers problem PROC Proof quadratic residue result rows self-complementary self-dual codes semimagic labeling sequence spanning tree starter strongly regular graphs subgraph of G subsets subsquare Suppose Theorem triple two-graph unique values vector vertex