منابع مشابه
Minimal 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 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.
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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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OF DISSERTATION Submitted in the partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate School of Arts and Sciences of Northeastern University, April 2009
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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: Combinatorics, Probability and Computing
سال: 2016
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548316000316