منابع مشابه
Hypercube subgraphs with local detours
A minimal detour subgraph of the n-dimensional cube is a spanning subgraph G of Qn having the property that for vertices x, y of Qn, distances are related by dG(x; y) dQn(x; y) + 2. For a spanning subgraph G of Qn to be a local detour subgraph, we require only that the above inequality be satis ed whenever x and y are adjacent in Qn. Let f(n) (respectively, fl(n) ) denote the minimum number of ...
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A spanning subgraph H of a graph G is a 2-detour subgraph of G if for each x, y ∈ V (G), dH(x, y) ≤ dG(x, y) + 2. We prove a conjecture of Erdős, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2-detour subgraph of the n-dimensional hypercube Qn has at least c log2 n · 2n edges.
متن کاملMinimal Saturated Subgraphs of the Hypercube
Within the hypercube Qn, we investigate bounds on the saturation number of a forbidden graph G, defined as the minimum number of edges in a subgraph H of Qn that is both G-free and has the property that the addition of any e⋲ E(Qn) n E(H) creates G. For all graphs G, we find a lower bound based on the minimum degree of non-leaves. For upper bounds, we first examine general graphs and derive con...
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A celebrated theorem of Turán asserts that every graph on n vertices with more than r− 1 2r n 2 edges contains a copy of a complete graph Kr+1. In this paper we consider the following more general question. Let G be a Kr+1-free graph of order n and let α be a constant, 0 < α 1. How dense can every induced subgraph of G on αn vertices be? We prove the following local density extension of Turán’s...
متن کاملOn 14-Cycle-Free Subgraphs of the Hypercube
It is shown that the size of a subgraph of Qn without a cycle of length 14 is of order o(|E(Qn)|). 1 Subgraphs of the hypercube with no C4 or C6 For given two graphs, Q and P , let ex(Q,P ) denote the generalized Turán number, i.e., the maximum number of edges in a P -free subgraph of Q. The n-dimensional hypercube, Qn, is the graph with vertex-set {0, 1}n and edges assigned between pairs diffe...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 1999
ISSN: 0364-9024,1097-0118
DOI: 10.1002/(sici)1097-0118(199902)30:2<101::aid-jgt4>3.3.co;2-0