If a graph has bounded clique number and sufficiently large chromatic number, what can we
say about its induced subgraphs? András Gyárfás made a number of challenging …

A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. A 20-
year-old conjecture asserts that for every fixed k, the maximum number of edges in a k-quasi …

Let ω (G) and χ (G) denote the clique number and chromatic number of a graph G,
respectively. The disjointness graph of a family of curves (continuous arcs in the plane) is …

We prove that for every integer t\geqslant 1 t⩾ 1, the class of intersection graphs of curves in
the plane each of which crosses a fixed curve in at least one and at most t points is χ χ …

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 …

Recently, it was proved that triangle-free intersection graphs of nn line segments in the
plane can have chromatic number as large as Θ (\log\log n) Θ (log log n). Essentially the …

An outerstring graph is an intersection graph of curves lying in a halfplane with one endpoint
on the boundary of the halfplane. It is proved that the outerstring graphs are χ-bounded, that …

An outerstring graph is an intersection graph of curves that lie in a common half-plane and
have one endpoint on the boundary of that half-plane. We prove that the class of outerstring …

Conflict-free coloring (in short, CF-coloring) of a graph G=(V, E) G=(V, E) is a coloring of V
such that the punctured neighborhood of each vertex contains a vertex whose color differs …

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