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We study a graph coloring problem motivated by a fun Sudoku-style puzzle. Given a bipartition of the edges of a graph into near and far sets and an integer threshold t, a threshold-coloring of the graph is an assignment of integers to the vertices so that endpoints of near edges differ by t or less, while endpoints of far edges differ by more than t. We… (More)

We study a variant of intersection representations with unit balls, that is, unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far sets, the goal is to represent the vertices of the graph by unit balls so that the balls representing two adjacent vertices intersect if and… (More)

- Abhijit Saha, Zhe Wang, +13 authors Tayeb Zaidi
- 2016

The Arizona-NOAO Temporal Analysis and Response to Events System (ANTARES) is a joint effort of NOAO and the Department of Computer Science at the University of Arizona to build prototype software to process alerts from time-domain surveys, especially LSST, to identify those alerts that must be followed up immediately. Value is added by annotating incoming… (More)

We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time… (More)

We study contact representations of non-planar graphs in which ver-tices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We present a liner-time algorithm constructing a representation of a 3-connected planar graph, its dual, and the vertex-face incidence graph with… (More)

- Muhammad Jawaherul Alam, Steven Chaplick, +4 authors Jackson Toeniskoetter
- Discrete Applied Mathematics
- 2017

In this paper we study threshold-coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. A pair of vertices with a small difference in their colors implies that the edge between them is present, while a pair of vertices with a big color difference implies that the edge is… (More)

We study a variant of intersection representations with unit balls: unit disks in the plane and unit intervals on the line. Given a planar graph and a bipar-tition of the edges of the graph into near and far edges, the goal is to represent the vertices of the graph by unit-size balls so that the balls for two adjacent vertices intersect if and only if the… (More)

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