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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| Vydané v: | Discrete mathematics Ročník 347; číslo 1; s. 113699 |
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Elsevier B.V
01.01.2024
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 113699 |
| Author | Trotignon, Nicolas Hoàng, Chính T. |
| Author_xml | – sequence: 1 givenname: Chính T. orcidid: 0000-0001-6782-1194 surname: Hoàng fullname: Hoàng, Chính T. organization: Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada – sequence: 2 givenname: Nicolas surname: Trotignon fullname: Trotignon, Nicolas email: nicolas.trotignon@ens-lyon.fr organization: Univ Lyon, EnsL, UCBL, CNRS, LIP, F-69342, LYON Cedex 07, France |
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| Cites_doi | 10.1007/s002249910009 10.1007/s00373-013-1290-3 10.1016/0022-0000(93)90004-G 10.1007/s11083-010-9174-0 10.1142/S0129054100000260 10.1002/jgt.22111 10.1016/j.jcss.2017.06.005 10.1016/j.jctb.2005.10.006 10.1016/j.jctb.2017.09.012 10.1002/jgt.22635 10.1016/j.ejc.2019.103002 10.1007/s00453-020-00747-x 10.1016/j.dam.2016.04.003 10.1016/j.dam.2009.07.010 10.1002/jgt.22146 10.1016/j.disc.2017.09.013 10.1002/jgt.22666 |
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| Keywords | Cliquewidth Rankwidth Even-hole-free graphs Dilworth number Rings |
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| Snippet | We describe several graphs with arbitrarily large rankwidth (or equivalently with arbitrarily large cliquewidth). Korpelainen, Lozin, and Mayhill [Split... |
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| SubjectTerms | Cliquewidth Computer Science Dilworth number Even-hole-free graphs Mathematics Rankwidth Rings |
| Title | A class of graphs with large rankwidth |
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