Graphic sequences with unique realization
نویسندگان
چکیده
منابع مشابه
Graphic sequences with a realization containing a generalized friendship graph
Gould, Jacobson and Lehel (Combinatorics, Graph Theory and Algorithms, Vol.I (1999) 451–460) considered a variation of the classical Turán-type extremal problems as follows: for any simple graph H, determine the smallest even integer σ(H, n) such that every n-term graphic sequence π = (d1, d2, . . . , dn) with term sum σ(π) = d1 + d2 + · · ·+ dn ≥ σ(H, n) has a realization G containing H as a s...
متن کاملGraphic sequences with a realization containing a complete multipartite subgraph
A nonincreasing sequence of nonnegative integers π = (d1, d2, ..., dn) is graphic if there is a (simple) graph G of order n having degree sequence π. In this case, G is said to realize π. For a given graph H, a graphic sequence π is potentially H-graphic if there is some realization of π containing H as a (weak) subgraph. Let σ(π) denote the sum of the terms of π. For a graph H and n ∈ Z+, σ(H,...
متن کاملGraphic Sequences with a Realization Containing a Union of Cliques
An integer sequence π is said to be graphic if it is the degree sequence of some simple graph G. In this case we say that G is a realization of π. Given a graph H, and a graphic sequence π we say that π is potentially H-graphic if there is some realization of π that contains H as a subgraph. We define σ(H, n) to be the minimum even integer such that every graphic sequence with sum at least σ(H,...
متن کاملGraphic Sequences with a Realization Containing a Friendship Graph
For any simple graph H, let σ(H,n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex graph G witnessing π that contains H as a weak subgraph. Let Fk denote the friendship graph on 2k+1 vertices, that is, the graph of k triangles intersecting in a single vertex. In this paper, for n sufficiently large, σ(...
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 ∆ ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1975
ISSN: 0095-8956
DOI: 10.1016/0095-8956(75)90072-6