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06/22/2023
Decomposition of Geometric Graphs into Star Forests
We solve a problem of Dujmović and Wood (2007) by showing that a complet...
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12/04/2021
Quasiplanar graphs, string graphs, and the Erdos-Gallai problem
An r-quasiplanar graph is a graph drawn in the plane with no r pairwise ...
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08/25/2021
On the number of edges of separated multigraphs
We prove that the number of edges of a multigraph G with n vertices is a...
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04/18/2019
Planar Point Sets Determine Many Pairwise Crossing Segments
We show that any set of n points in general position in the plane determ...
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08/30/2018
The number of crossings in multigraphs with no empty lens
Let G be a multigraph with n vertices and e>4n edges, drawn in the plane...
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03/18/2018
Almost all string graphs are intersection graphs of plane convex sets
A string graph is the intersection graph of a family of continuous arcs...
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12/08/2017
Tilings of the plane with unit area triangles of bounded diameter
There exist tilings of the plane with pairwise noncongruent triangles of...
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11/13/2017
Tilings with noncongruent triangles
We solve a problem of R. Nandakumar by proving that there is no tiling o...
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08/07/2017
