Boxicity of Series Parallel Graphs

dc.creatorBohra, Ankur
dc.creatorChandran, L. Sunil
dc.creatorRaju, J. Krishnam
dc.date2005-09-24
dc.date.accessioned2026-07-07T06:19:09Z
dc.date.available2026-07-07T06:19:09Z
dc.descriptionThe three well-known graph classes, planar graphs (P), series-parallel graphs(SP) and outer planar graphs(OP) satisfy the following proper inclusion relation: OP C SP C P. It is known that box(G) <= 3 if G belongs to P and box(G) <= 2 if G belongs to OP. Thus it is interesting to decide whether the maximum possible value of the boxicity of series-parallel graphs is 2 or 3. In this paper we construct a series-parallel graph with boxicity 3, thus resolving this question. Recently Chandran and Sivadasan showed that for any G, box(G) <= treewidth(G)+2. They conjecture that for any k, there exists a k-tree with boxicity k+1. (This would show that their upper bound is tight but for an additive factor of 1, since the treewidth of any k-tree equals k.) The series-parallel graph we construct in this paper is a 2-tree with boxicity 3 and is thus a first step towards proving their conjecture.
dc.description10 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/math/0509581
dc.identifierhttp://arxiv.org/abs/math/0509581
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94981
dc.subjectCombinatorics
dc.subject05C62
dc.titleBoxicity of Series Parallel Graphs
dc.typetext

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