A General Lower Bound for Potentially H-Graphic Sequences
نویسندگان
چکیده
منابع مشابه
A General Lower Bound for Potentially H-Graphic Sequences
We consider an extremal problem for graphs as introduced by Erdős, Jacobson and Lehel in [7]. Let π be an n-element graphic sequence. Let H be a graph. We wish to determine the smallest m such that any nterm graphic sequence π whose terms sum to at least m has some realization containing H as a subgraph. Denote this value m by σ(H, n). For an arbitrarily chosen H, we give a construction that yi...
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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 3-partite 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] ...
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متن کاملPotentially H-bigraphic sequences
We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X ∪ Y, E) such that A and B are the degrees of the vertices in X and Y , respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A. Given a bigraphic pair S, and a fixe...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2009
ISSN: 0895-4801,1095-7146
DOI: 10.1137/080715275