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Let ex * (D; H) denote the maximum number of edges in a connected graph with maximum degree D and no induced subgraph isomorphic to H. We prove that this is finite only when H is a disjoint union of paths,m in which case we provide crude upper and lower bounds. When H is the four-vertex path P4, we prove that the complete bipartite graph K D , ~ is the… (More)

Let ex (D; H) be the maximum number of edges in a connected graph with maximum degree D and no induced subgraph H; this is nite if and only if H is a disjoint union of paths. If the largest component of such an H has order m, then ex (D; H) = O(D 2 ex (D; P m)). Constructively, ex (D; qP m) = (qD 2 ex (D; P m)) if q > 1 and m > 2 (((qD 2) if m = 2). For H =… (More)

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