4 papers
Independent Chains in Acyclic Posets
Nika Salia, Christoph Spiegel, Casey Tompkins +1
We consider the problem of determining the maximum order of an induced vertex-disjoint union of cliques in a graph. More specifically, given some family of graphs of…
Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs
Maria Axenovich, Casey Tompkins, Lea Weber
For a bipartite graph G, let h(G) be the largest t such that either G or the bipartite complement of G contain K_{t,t}. For a class F of graphs, let h(F)= min {h(G): G\in F}. We sa…
Intersection Graphs of Rays and Grounded Segments
Jean Cardinal, Stefan Felsner, Tillmann Miltzow +2
We consider several classes of intersection graphs of line segments in the plane and prove new equality and separation results between those classes. In particular, we show that: (…
De Bruijn-Erdős type theorems for graphs and posets
Pierre Aboulker, Guillaume Lagarde, David Malec +2
A classical theorem of De Bruijn and Erdős asserts that any noncollinear set of n points in the plane determines at least n distinct lines. We prove that an analogue of this theore…