ul 2 00 6 An extremal problem on potentially K p , 1 , 1 - graphic sequences ∗
نویسنده
چکیده
A sequence S is potentially Kp,1,1 graphical if it has a realization containing a Kp,1,1 as a subgraph, where Kp,1,1 is a complete 3partite graph with partition sizes p, 1, 1. Let σ(Kp,1,1, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Kp,1,1, n) is potentially Kp,1,1 graphical. In this paper, we prove that σ(Kp,1,1, n) ≥ 2[((p + 1)(n − 1) + 2)/2] for n ≥ p + 2. We conjecture that equality holds for n ≥ 2p + 4. We prove that this conjecture is true for p = 3.
منابع مشابه
ul 2 00 6 An extremal problem on potentially K m − P k - graphic sequences ∗
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A sequence S is potentially Kp,1,1 graphical if it has a realization containing a Kp,1,1 as a subgraph, where Kp,1,1 is a complete 3partite graph with partition sizes p, 1, 1. Let σ(Kp,1,1, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Kp,1,1, n) is potentially Kp,1,1 graphical. In this paper, we prove that σ(Kp,1,1, n) ≥ 2[((p + 1)(n − 1) + 2)/2] f...
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A sequence S is potentiallyKp1,p2,...,pt graphical if it has a realization containing aKp1,p2,...,pt as a subgraph, whereKp1,p2,...,pt is a complete t-partite graph with partition sizes p1, p2, ..., pt(p1 ≥ p2 ≥ ... ≥ pt ≥ 1). Let σ(Kp1,p2,...,pt, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Kp1,p2,...,pt, n) is potentially Kp1,p2,...,pt graphical....
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