## Graph theory |

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1-factor adjacency matrix assigned augmenting path bipartite graph bound called chromatic number circuit complete graph components connected graph consider construct contradiction Corollary cut set degree sequence denote depth-first search determine digraph disjoint distance edges of G embedding eulerian eulerian circuit example exists extremal graph finite state machine G contains G is hamiltonian graph G graph of Figure graph of order Graph Theory hamiltonian cycle hence homeomorphic induced subgraph induction Input integer isomorphic labeled layered network least length Let G mapping Math maximum flow maximum matching maximum number Menger's theorem minimum weight nonadjacent vertices number of edges number of vertices obtain pair partial order planar graph problem Proof Prove ramsey number region result Section segment spanning trees step subgraph of G subset Suppose Theorem tournament vertices of degree vertices of G weighted path length zero