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- W4230188095 abstract "Let G be connected simple graph with diameter d(G). G is said v+-critical if d(G−v) is greater than d(G) for every vertex v of G. Let D′ = max {d(G−v) : v ∈ V(G)}. Boals et al. [Congressus Numerantium 72 (1990), 193—198] conjectured that if G is a v+-critical graph of diameter D, then D′ ≤ 2D − 1. They verified their conjecture for D = 2 and 3. In this paper we show that this conjecture is false for all D ≥ 4 and establish a sharp upper bound for D′. More specifically, we prove that D′ ≤ 3D − 3 for D = 4, 6, 8; and ; otherwise. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 117–131, 2003" @default.
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- W4230188095 date "2003-05-13" @default.
- W4230188095 modified "2023-09-26" @default.
- W4230188095 title "On vertex critical graphs with prescribed diameter" @default.
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- W4230188095 doi "https://doi.org/10.1002/jgt.10108" @default.
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