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2-connected abstract simplicial complex adjacent algorithm assume bipartite graph CCE-orientable chromatic polynomial Claim coloring combinatorial complete bipartite graph complete graph Computer connected graph consider construct contradiction Corollary critical set defined denote Department of Mathematics digraph discs disjoint distinct vertices dominating in G dominating set domination number edge of G edge-connectivity edge-magic elements exists Fibonacci matrix Figure finite formula G contains graph G graph of order Graph Theory hamiltonian Hence implies induced inequality isomorphic k-dominate labeling latin square Lemma Let G loops matrix of order matroid maximal minimum degree multipartite n-step dominated niche graph nP(Z number of vertices obtain p-cycle pair partite sets path planar graph points proof of Theorem Proposition prove quadrilateral Ramsey numbers result set of G Skolem sequences small 2-factor Steiner triple system strongly regular graph subgraph subset subsystems Suppose torus triple systems vector vertices of G