Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boxicity of Series Parallel Graphs   The 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.

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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol