%A Dabrowski, Konrad K.
%A Dross, François
%A Jeong, Jisu
%A Kanté, Mamadou Moustapha
%A Kwon, O-joung
%A Oum, Sang-il
%A Paulusma, Daniël
%D 2019
%T Tree pivot-minors and linear rank-width
%K
%X Treewidth and its linear variant path-width play a central role for the graph minor relation. Rank-width and linear rank-width do the same for the graph pivot-minor relation. Robertson and Seymour (1983) proved that for every tree T there exists a constant c T such that every graph of path-width at least c T contains T as a minor. Motivated by this result, we examine whether for every tree T there exists a constant d T such that every graph of linear rank-width at least d T contains T as a pivot-minor. We show that this is false if T is not a caterpillar, but true if T is the claw.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1298
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 577-583%V 88
%N 3
%@ 0862-9544
%8 2019-07-29