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acyclic adjacent approximation algorithm assignment assume biclique binary bipartite graph cell clique color colour schemes Combinatorial competition graph complete graph component Computer configuration conjecture consider construct contains Corollary decomposition defined definition degree denote digraph disjoint dominant edge dominating set domination number eB(y elements example exists Figure finite follows function given graph G Graph Theory grid graph hamiltonian hamiltonian cycle Hence hypercube induced induced subgraph integer interval graphs labeled Latin square least Lemma linear lower bound Math matrix matroid maximal convertible maximum number minimum niche graph niche number nodes NP-complete number of vertices obtained optimal pair partition permutation planar graph polynomial problem Proof quadtree result root route satisfies sequenced basis set sequence shortest path sign-nonsingular solution Steiner triple systems subgraph subset subtrees support sets Suppose t-clique Theorem token queue token request tournament traffic vector vertex Vizing's conjecture worst-case performance