
Universal Geometric Graphs
We introduce and study the problem of constructing geometric graphs that...
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Large Minors in Expanders
In this paper we study expander graphs and their minors. Specifically, w...
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Supercards, Sunshines and Caterpillar Graphs
The vertexdeleted subgraph Gv, obtained from the graph G by deleting t...
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Graphical Construction of Spatial Gibbs Random Graphs
We present a Spatial Gibbs Random Graphs Model that incorporates the int...
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Temporal Cliques admit Sparse Spanners
Let G=(G,λ) be a labeled graph on n vertices with λ:E_G→N a locally inj...
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Planar projections of graphs
We introduce and study a new graph representation where vertices are emb...
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Computing kModal Embeddings of Planar Digraphs
Given a planar digraph G and a positive even integer k, an embedding of ...
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Sparse universal graphs for planarity
We show that for every integer n≥ 1 there exists a graph G_n with (1+o(1))n vertices and n^1 + o(1) edges such that every nvertex planar graph is isomorphic to a subgraph of G_n. The best previous bound on the number of edges was O(n^3/2), proved by Babai, Chung, Erdős, Graham, and Spencer in 1982. We then show that for every integer n≥ 1 there is a graph U_n with n^1 + o(1) vertices and edges that contains induced copies of every nvertex planar graph. This significantly reduces the number of edges in a recent construction of the authors with Dujmović, Gavoille, and Micek.
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