**Cubic partial cubes from simplicial arrangements.**

D. Eppstein.

arXiv:math.CO/0510263.

*Electronic J. Combinatorics*13(1), Paper R79, 2006.We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.

**The Fibonacci dimension of a graph**.

S. Cabello, D. Eppstein, and S. Klavžar.

IMFM Preprint 1084, Institute of Mathematics, Physics and Mechanics, Univ. of of Ljubljana, 2009.

arXiv:0903.2507.

*Electronic J. Combinatorics*18(1), Paper P55, 2011.We investigate isometric embeddings of other graphs into Fibonacci cubes, graphs formed from the families of fixed-length bitstrings with no two consecutive ones.

**Densities of minor-closed graph families**.

D. Eppstein.

arXiv:1009.5633.

*Electronic J. Combinatorics*17(1), Paper R136, 2010.For every minor-closed graph family (such as the family of planar graphs), there is a constant c such that the maximum number of edges in an n-vertex graph in the family is

*c*(*n*+*o*(*n*); for instance, for planar graphs,*c*= 3. We call*c*the limiting density of the family, and we study the set of all limiting densities of all minor-closed graph families. We show that this set of limiting densities is closed and well-ordered, with order type at least ω^{ω}, and we find an exact description of the members of this set up to its first two cluster points 1 and 3/2.**Grid minors in damaged grids**.

D. Eppstein.

arXiv:1303.1136.

*Electronic J. Combinatorics*21(3), Paper P3.20, 2014.We give tight bounds on the size of the largest remaining grid minor in a grid graph from which a given number of vertices have been deleted, and study several related problems.

**Existence and hardness of conveyor belts**.

M. Baird, S. C. Billey, E. Demaine, M. Demaine, D. Eppstein, S. P. Fekete, G. Gordon, S. Griffin, J. S. B. Mitchell, and J. P. Swanson.

arXiv:1908.07668.

*Electronic J. Combinatorics*27 (4), Paper P4.25, 2020.A conveyor belt is a tight simple closed curve that touches each of a given set of disjoint disks. We show that certain special families of disks always have a conveyor belt, but that it is NP-complete to tell whether one exists for arbitrary families of disks. It is always possible to add a linear number of "guide disks" to a given set of disks to allow them to be connected by a conveyor belt.

Journals – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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