The Edge Spectrum of K4-Saturated Graphs
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چکیده
Any H-free graph G is called H-saturated if the addition of any edge e / ∈ E(G) results in H as a subgraph of G. The minimum size of an H-saturated graph on n vertices is denoted by sat(n,H). The edge spectrum for the family of graphs with property P is the set of all sizes of graphs with property P . In this paper, we find the edge spectrum of K4-saturated graphs. We also show that if G is a K4-saturated graph, then either G ∼= K1,1,n−2 or δ(G) ≥ 3, and we show the exact structure of a K4-saturated graph with κ(G) = 2 and κ(G) = 3.
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تاریخ انتشار 2011