A ug 2 00 4 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 conjectured that equality holds for n ≥ 2p + 4. We proved that this conjecture is true for p = 3.
منابع مشابه
2 4 A ug 2 00 4 An extremal problem on potentially K p 1 , p 2 , . . . , p t - graphic sequences ∗
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....
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 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...
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Let Kk, Ck, Tk, and Pk denote a complete graph on k vertices, a cycle on k vertices, a tree on k + 1 vertices, and a path on k + 1 vertices, respectively. Let Km−H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of Km). 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 s...
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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تاریخ انتشار 2004