Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  857.05027
Autor:  Erdös, Pál; Hamburger, Peter; Pippert, Raymond E.; Weakley, William D.
Title:  Hypercube subgraphs with minimal detours. (In English)
Source:  J. Graph Theory 23, No.2, 119-128 (1996).
Review:  What happens to distances in a graph when moving to a subgraph? In an n-dimensional hypercube some distance always increases by at least 2. The minimum number of edges for the subgraph, necessary to keep such detours within 2 for all vertex-pairs, is shown to be at most max{{n+5\over 4n}; {3\over \sqrt{2n}}} of the number of n-hypercube edges, and at least (4-{14n-38\over n2+n-10})2n-1.
Reviewer:  F.Plastria (Brussels)
Classif.:  * 05C12 Distance in graphs
                   05C35 Extremal problems (graph theory)
                   68R10 Graph theory in connection with computer science
Keywords:  subgraph; hypercube; distance; detours

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