Intersection Graphs of Maximal Sub-polygons of k-Lizards
Name
373_2023_2670_ReferencePDF.pdf
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Author(s)
Daugherty, Caroline
Laison, Joshua D.
Robinson, Rebecca
Salois, Kyle
Date Issued
June 27, 2023
Publisher
Springer Japan
Citation
Graphs and Combinatorics. 2023 Jun 27;39(4):75
Version
Author's final manuscript
Abstract
Abstract
We introduce k-maximal sub-polygon graphs (k-MSP graphs), the intersection graphs of maximal polygons contained in a polygon with sides parallel to a regular 2k-gon. We prove that all complete graphs are k-MSP graphs for all
$$k>1$$
k
>
1
; trees are 2-MSP graphs; trees are k-MSP graphs for
$$k>2$$
k
>
2
if and only if they are caterpillars; and n-cycles are not k-MSP graphs for
$$n>3$$
n
>
3
and
$$k>1$$
k
>
1
. We derive bounds for which j-cycles appear as induced subgraphs of k-MSP graphs. As our main result, we construct examples of graphs which are k-MSP graphs and not j-MSP graphs for all
$$k>1$$
k
>
1
,
$$j>1$$
j
>
1
,
$$k \ne j$$
k
≠
j
.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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DOI of Published Version
https://doi.org/10.1007/s00373-023-02670-8
