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There is a tree with degree sequence (3, 2, 2, 2, 2, 2, 1). ) There is a simple graph with 100 vertices and 5000 edges. A graph has degree sequence (8, 6, 5, 4, 3, 2). It can not have a closed Euleriantrail. ) Let n ≥ 2 be an ingeter. It is possible for a tree of n vertices to have an open Eulerian trail. Let n ≥ 2 be an ingeter. It is possible for a tree of n vertices to have a closed Eulerian trail. (f) Let G be a bipartite graph with bipartition X, Y, and [X] ‡ |Y]. Then G cannot have a Hamilton cycle. (g) Let G be a bipartite graph with bipartition X, Y, and X| = |Y. Then G cannot have a Hamilton path. (h) If G is a bipartite graph, then p(G) = c(G), i.e., the matching number equals the vertex cover number. (i) If G is not a bipartite graph, then p(G) < c(G), i.e., the matching number must be smaller than the vertex cover number. (j) The number of ways to triangulate a polygon with (n + 2) sides is (²).n+1

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