ores theorem. A connected graph with N vertices is said to satisfy Ores condition if
Chapter 6, Problem 73(choose chapter or problem)
ores theorem. A connected graph with N vertices is said to satisfy Ores condition if deg1X2 + deg1Y2 N for every pair of vertices X and Y of the graph. Ores theorem states that if a graph satisfies Ores condition, then it has a Hamilton circuit. (a) Explain why the complete bipartite graph Kn, n (see Exercise 71) satisfies Ores condition. (b) Explain why for m n, the complete bipartite graph Km, n (see Exercise 71) does not satisfy Ores condition. (c) Ores condition is sufficient to guarantee that a connected graph has a Hamilton circuit but is not a necessary condition. Give an example of a graph that has a Hamilton circuit but does not satisfy Ores condition.
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