Chandran, Sunil L and Francis, Mathew C and Suresh, Santhosh
(2009)
*Boxicity of Halin graphs.*
In: Discrete Mathematics, 309
(10).
pp. 3233-3237.

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## Abstract

A k-dimensional box is the Cartesian product R-1 x R-2 x ... x R-k where each R-i is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such a way that the graph has a planar embedding. We prove that if G is a Halin graph that is not isomorphic to K-4, then box(G) = 2. In fact, we prove the stronger result that if G is a planar graph formed by connecting the leaves of any tree in a simple cycle, then box(G) = 2 unless G is isomorphic to K4 (in which case its boxicity is 1).

Item Type: | Journal Article |
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Additional Information: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Halin graphs;Boxicity;Intersection graphs;Planar graphs. |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation) |

Date Deposited: | 10 Jul 2009 10:35 |

Last Modified: | 19 Sep 2010 05:35 |

URI: | http://eprints.iisc.ernet.in/id/eprint/21008 |

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