2 4 A ug 2 00 4 An extremal problem on potentially K p 1 , p 2 , . . . , p t - graphic sequences ∗
نویسنده
چکیده
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. In this paper, we prove that σ(Kp1,p2,...,pt, n) ≥ 2[((2p1 + 2p2 + ... + 2pt − p1 − p2 − ... − pi − 2)n − (p1 + p2 + ... + pt − pi)(pi + pi+1 + ... + pt − 1) + 2)/2] for n ≥ p1 + p2 + ...+ pt, i = 2, 3, ..., t.
منابع مشابه
A ug 2 00 4 An extremal problem on potentially K p , 1 , 1 - graphic sequences ∗
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...
متن کاملul 2 00 6 An extremal problem on potentially K p , 1 , 1 - graphic sequences ∗
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...
متن کاملul 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...
متن کاملSe p 20 04 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 conjectured that equality holds for n ≥ m ≥ k + 1 ≥ 4. ...
متن کاملM ar 2 00 6 An Extremal Problem On Potentially K r + 1 − ( kP 2 ⋃ tK 2 ) - graphic Sequences ∗
A sequence S is potentially Km − H-graphical if it has a realization containing a Km − H as a subgraph. Let σ(Km − H,n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Km−H,n) is potentially Km−H-graphical. In this paper, we determine σ(Kr+1−(kP2 ⋃ tK2), n) for n ≥ 4r+10, r+1 ≥ 3k+2t, k+t ≥ 2, k ≥ 1, t ≥ 0 .
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