Strong isometric dimension, biclique coverings, and Sperner's theorem

Dalibor Fronček; Janja Jerebic; Sandi Klavžar; Petr Kovář

doi:10.1017/S0963548306007711

Strong isometric dimension, biclique coverings, and Sperner's theorem

Dalibor Fronček, Janja Jerebic, Sandi Klavžar, Petr Kovář

Mathematics & Statistics

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Abstract

The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's theorem, the strong isometric dimension of the Hamming graphs K₂□ K_n is determined.

Original language	English (US)
Pages (from-to)	271-275
Number of pages	5
Journal	Combinatorics Probability and Computing
Volume	16
Issue number	2
DOIs	https://doi.org/10.1017/S0963548306007711
State	Published - Mar 2007

Bibliographical note

Funding Information:
† Supported by the University of Minnesota Duluth Grant 177–1009. ‡Supported by the Ministry of Science of Slovenia under the grant Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana.

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abstract = "The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's theorem, the strong isometric dimension of the Hamming graphs K2□ Kn is determined.",

author = "Dalibor Fron{\v c}ek and Janja Jerebic and Sandi Klav{\v z}ar and Petr Kov{\'a}{\v r}",

note = "Funding Information: † Supported by the University of Minnesota Duluth Grant 177–1009. ‡Supported by the Ministry of Science of Slovenia under the grant Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana.",

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AU - Klavžar, Sandi

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Strong isometric dimension, biclique coverings, and Sperner's theorem

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