In this paper we explore fundamental problems in randomized communication complexity such as computing SetIntersection on sets of size $k$ and EqualityTesting between vectors length $k$. Saglam ...

We study on-line colorings of certain graphs given as intersection graphs of objects “between two lines”, i.e., there is a pair of horizontal lines such that each object of the representation is a connected set contained in the strip between the lines and touches both. Some of the graph classes admitting such a representation are permutation graphs (segments), interval graphs (axisaligned recta...

A graph is chordal if and only if it is the intersection graph of some family of subtrees of a tree. Applying “tolerance” allows larger families of graphs to be represented by subtrees. A graph G is in the family [∆, d, t] if there is a tree with maximum degree ∆ and subtrees corresponding to the vertices of G such that each subtree has maximum degree at most d and vertices of G are adjacent if...