Se p 20 04 An extremal problem on potentially K m − P k - graphic sequences ∗
نویسنده
چکیده
A sequence S is potentially Km−Pk graphical if it has a realization containing a Km −Pk as a subgraph. Let σ(Km −Pk, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Km−Pk, n) is potentially Km−Pk graphical. In this paper, we prove that σ(Km−Pk, n) ≥ (2m−6)n−(m−3)(m−2)+2, for n ≥ m ≥ k + 1 ≥ 4. We conjectured that equality holds for n ≥ m ≥ k + 1 ≥ 4. We proved that this conjecture is true for m = k + 1 = 5 and m = k + 2 = 5.
منابع مشابه
ul 2 00 6 An extremal problem on potentially K m − P k - graphic sequences ∗
A sequence S is potentially Km−Pk graphical if it has a realization containing a Km −Pk as a subgraph. Let σ(Km −Pk, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Km−Pk, n) is potentially Km−Pk graphical. In this paper, we prove that σ(Km−Pk, n) ≥ (2m−6)n−(m−3)(m−2)+2, for n ≥ m ≥ k + 1 ≥ 4. We conjecture that equality holds for n ≥ m ≥ k + 1 ≥ 4. W...
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تاریخ انتشار 2004