On multigraphic and potentially multigraphic sequences
نویسندگان
چکیده
منابع مشابه
Multigraphic degree sequences and supereulerian graphs, disjoint spanning trees
A sequence d = (d1, d2, . . . , dn) is multigraphic if there is a multigraph G with degree sequence d, and such a graph G is called a realization of d. In this paper, we prove that a nonincreasing multigraphic sequence d = (d1, d2, . . . , dn) has a realization with a spanning eulerian subgraph if and only if either n = 1 and d1 = 0, or n ≥ 2 and dn ≥ 2, and that d has a realization G such that...
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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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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...
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: Acta Universitatis Sapientiae, Informatica
سال: 2017
ISSN: 2066-7760
DOI: 10.1515/ausi-2017-0003