Seven criteria for integer sequences being graphic
نویسندگان
چکیده
منابع مشابه
One-Pass Graphic Approximation of Integer Sequences
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of the sequence. This approximation scheme is fast, requiring only one pass through the sequence, and produces small probability distribution distances for large ...
متن کاملPacking of Graphic Sequences
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 ∆ ...
متن کاملSome 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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Bixby and Cunningham showed that a 3-connected binary matroid M is graphic if and only if every element belongs to at most two non-separating cocircuits. Likewise, Lemos showed that such a matroid M is graphic if and only if it has exactly r(M) + 1 nonseparating cocircuits. Hence the presence inM of either an element in at least three non-separating cocircuits, or of at least r(M) + 2 non-separ...
متن کاملSeven Staggering Sequences
0. Introduction When the Handbook of Integer Sequences came out in 1973, Philip Morrison gave it an enthusiastic review in the Scientific American and Martin Gardner was kind enough to say in hisMathematical Games column for July 1974 that “every recreational mathematician should buy a copy forthwith.” That book contained 2372 sequences. Today the On-Line Encyclopedia of Integer Sequences (or O...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 1991
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.3190150209