Constructive extensions of two results on graphic sequences
نویسندگان
چکیده
منابع مشابه
Some Problems on Graphic Sequences
A nonnegative integer sequence π is graphic if there is some simple graph G having degree sequence π. In that case, G is said to realize or be a realization of π. A given degree sequence may have many realizations, and it has been of interest to examine the spectrum of properties and parameters that occur across these realizations. In this survey, we present five areas of recent research on gra...
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Let π1 and π2 be graphic n-tuples, with π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) (they need not be monotone). We say that π1 and π2 pack if there exist edge-disjoint graphs G1 and G2 with vertex set {v1, . . . , vn} such that the degrees of vi in G1 and G2 are d (1) i and d (2) i , respectively. We prove that two graphic n-tuples pack if ∆ ≤ √ 2δn− (δ−1), where ∆ ...
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In this paper, we characterize the potentially (K4 − e)-graphic sequences where K4 − e is the graph obtained from K4 by removing one edge. This characterization implies a theorem due to C. H. Lai (Australas. J. Combin. 24 (2001), 123–127) and a characterization of potentially C4graphic sequences due to R. Luo (Ars Combin. 64 (2002), 301–318).
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A sequence 1l = (d 1 ,d 2 , ... ,d n) of positive integers is said to be graphic if there exists a simple graph G such that 1£ is the degree sequence of G. For a specified property P of graphs. a sequence 1l = (d 1 ,d 2 • ... • d n) of positive integers is said to be potentially P-graphic if 1l is graphic and there exists a realization of 1l with the property P. In this paper we characterize po...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.06.017