Abstract
AbstractLet 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 KD,D is the unique extremal graph. Furthermore, if G is a connected P4‐free graph with maximum degree D and clique number ω, then G has at most D2 − D(ω − 2)/2 edges. © 1993 John Wiley & Sons, Inc.
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