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ArticleOriginal scientific text

Title

On the rainbow connection of Cartesian products and their subgraphs

Authors 1, 2, 3

Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
  2. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia
  3. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana

Abstract

Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above by the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rainbow connection number as small as possible compared to the rainbow connection of the hypercube are constructed. The concept of c-strong rainbow connected coloring is introduced. In particular, it is proved that the so-called Θ-coloring of an isometric subgraph of a hypercube is its unique optimal c-strong rainbow connected coloring.

Keywords

ENG
rainbow connection, strong rainbow connection, Cartesian product of graphs, isometric subgraph, hypercube

Bibliography

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Discussiones Mathematicae Graph Theory
2012/32/4
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Pages:
783-793
Main language of publication
English
Received
2011-06-08
Accepted
2012-02-06
Published
2012

DOI: 10.7151/dmgt.1644

Exact and natural sciences