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1) The graph G has 6 vertices with degrees 2, 2, 3, 4, 4, 5. How many edges does G have? 2) A connected graph G has 10 vertices. With which of the following extra conditions must G be a tree? a) G has at least 9 edges. b) G has at most 9 edges. c) G is bipartite. d) G has at least one circuit. 3) Which could be the degree sequence of a graph with 5 vertices? a) 1, 1, 1, 1, 1 b) 4, 3, 2, 1, 0 c) 3, 3, 1, 1, 0 d) 4, 4, 4, 3, 3 4) If
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(a) A graph has six vertices every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains a monochromatic triangle. (b) Is the result of (a) true for a graph with five vertices? Explain. | Numerade
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