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Grounded L-graphs are polynomially -bounded
James Davies, Tomasz Krawczyk, Rose McCarty +1
A grounded L-graph is the intersection graph of a collection of "L" shapes whose topmost points belong to a common horizontal line. We prove that every grounded L-graph with clique…
Colouring polygon visibility graphs and their generalizations
James Davies, Tomasz Krawczyk, Rose McCarty +1
Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with…
Dense induced subgraphs of dense bipartite graphs
Rose McCarty
We prove that every bipartite graph of sufficiently large average degree has either a -subgraph or an induced subgraph of average degree at least and girth at least $6…
Sublinear separators in intersection graphs of convex shapes
Zdenek Dvorak, Rose McCarty, Sergey Norin
We give a natural sufficient condition for an intersection graph of compact convex sets in R^d to have a balanced separator of sublinear size. This condition generalizes several pr…
The grid theorem for vertex-minors
Jim Geelen, O-Joung Kwon, Rose McCarty +1
We prove that, for each circle graph , every graph with sufficiently large rank-width contains a vertex-minor isomorphic to .
Circle graphs are quadratically -bounded
James Davies, Rose McCarty
We prove that the chromatic number of a circle graph with clique number is at most .