Potentially K m — G-graphical sequences: A survey
نویسندگان
چکیده
منابع مشابه
. C O ] 3 0 Se p 20 09 Potentially K m − G - graphical Sequences : A Survey ∗
The set of all non-increasing nonnegative integers sequence π = (d(v1), d(v2), ..., d(vn)) is denoted by NSn. A sequence π ∈ NSn is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NSn is denoted by GSn. A graphical sequence π is potentially H-graphical if there is a realizatio...
متن کاملA ug 2 00 3 A note on potentially K 4 − e graphical sequences ∗
A sequence S is potentially K4 − e graphical if it has a realization containing a K4 − e as a subgraph. Let σ(K4 − e, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(K4 − e, n) is potentially K4 − e graphical. Gould, Jacobson, Lehel raised the problem of determining the value of σ(K4 − e, n). In this paper, we prove that σ(K4 − e, n) = 2[(3n− 1)/2] fo...
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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 کاملA note on potentially K4-e graphical sequences
A sequence S is potentially K4 e graphical if it has a realization containing a K4 e as a subgraph. Let 0'(K4 e, n) denote the smallest degree sum such that every n-term graphical sequence S with O'(S) 2: a(I{4 e, n) is potentially K4 e graphical. Gould, Jacobson, Lehel raised the problem of determining the value of 0'(K4 e, n). In this paper, we prove that 0'(K4 e, n) = 2[(317, 1)/2] for 17, 2...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2009
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-009-0074-7