Graphic sequences with a realization containing a complete multipartite subgraph
نویسندگان
چکیده
منابع مشابه
Graphic 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 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 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 کاملA neighborhood condition which implies the existence of a complete multipartite subgraph
The complete multipartite graph with d partite sets, each containing m vertices, will be denoted by K(d; m). If all of the partite sets are not of the same cardinality, the graph K(mi, m2, . . . . md) is the complete d-partite graph with m, vertices in each partite sets, 1 <i<d. The special case where mi= 1 for every i, yields the complete graph on d vertices and is denoted by Kd. The join of g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.10.047