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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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|
|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|
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