A class of graphs with large rankwidth

We describe several graphs with arbitrarily large rankwidth (or equivalently with arbitrarily large cliquewidth). Korpelainen, Lozin, and Mayhill [Split permutation graphs, Graphs and Combinatorics, 30(3):633–646, 2014] proved that there exist split graphs with Dilworth number 2 with arbitrarily lar...

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Bibliographic Details
Published in:Discrete mathematics Vol. 347; no. 1; p. 113699
Main Authors: Hoàng, Chính T., Trotignon, Nicolas
Format: Journal Article
Language:English
Published: Elsevier B.V 01.01.2024
Elsevier
Subjects:
Cliquewidth
Computer Science
Dilworth number
Even-hole-free graphs
Mathematics
Rankwidth
Rings
Cliquewidth
Rankwidth
Even-hole-free graphs
Dilworth number
Rings
ISSN:0012-365X, 1872-681X
Online Access:Get full text
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Summary:We describe several graphs with arbitrarily large rankwidth (or equivalently with arbitrarily large cliquewidth). Korpelainen, Lozin, and Mayhill [Split permutation graphs, Graphs and Combinatorics, 30(3):633–646, 2014] proved that there exist split graphs with Dilworth number 2 with arbitrarily large rankwidth, but without explicitly constructing them. We provide an explicit construction. Maffray, Penev, and Vušković [Coloring rings, Journal of Graph Theory 96(4):642-683, 2021] proved that graphs that they call rings on n sets can be colored in polynomial time. We show that for every fixed integer n≥3, there exist rings on n sets with arbitrarily large rankwidth. When n≥5 and n is odd, this provides a new construction of even-hole-free graphs with arbitrarily large rankwidth.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2023.113699