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19922026
Showing 2019 · math.COShow all

11 papers · 2 filters

math.CO2019★ 1 cited

On strong infinite Sidon and sets and random sets of integers

David Fabian, Juanjo Rué, Christoph Spiegel

A set of integers is an -strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on , more specifically if $…

math.CO2019★ 3 cited

Hamiltonicity of random graphs in the stochastic block model

Michael Anastos, Alan Frieze, Pu Gao

We study the Hamiltonicity of the following model of a random graph. Suppose that we partition [n] into V_1,V_2,...,V_k and add edge {x,y} to our graph with probability p if there…

math.CO2019★ 3 cited

Exploring Projective Norm Graphs

Tomas Bayer, Tamás Mészáros, Lajos Rónyai +1

The projective norm graphs provide tight constructions for the Turán number of complete bipartite graphs with . In this paper we determine thei…

math.CO2019★ 1 cited

Minimal Representations of Order Types by Geometric Graphs

Oswin Aichholzer, Martin Balko, Michael Hoffmann +8

In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order ty…

math.CO2019

Unimodular covers of 3-dimensional parallelepipeds and Cayley sums

Giulia Codenotti, Francisco Santos

We show that the following classes of lattice polytopes have unimodular covers, in dimension three: the class of parallelepipeds, the class of centrally symmetric polytopes, and th…

math.CO2019★ 6 cited

A local maximizer for lattice width of -dimensional hollow bodies

Gennadiy Averkov, Giulia Codenotti, Antonio Macchia +1

The second and fourth authors have conjectured that a certain hollow tetrahedron of width attains the maximum lattice width among all three-dimensional convex bodies…

math.CO2019★ 3 cited

A new face iterator for polyhedra and more general finite locally branched lattices

Jonathan Kliem, Christian Stump

We discuss a new memory-efficient depth-first algorithm and its implementation that iterates over all elements of a finite locally branched lattice. This algorithm can be applied t…

math.CO2019★ 1 cited

Characterization of the response maps of alternating-current networks

Günter Rote

In an alternating-current network, each edge has a complex "conductance" with positive real part. The response map is the linear map from the vector of voltages at a subset of "bou…

math.CO2019★ 3 cited

The covering radius and a discrete surface area for non-hollow simplices

Giulia Codenotti, Francisco Santos, Matthias Schymura

We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of in dimension , achieved by the "stand…

math.CO2019★ 4 cited

Finding any given 2-factor in sparse pseudorandom graphs efficiently

Jie Han, Yoshiharu Kohayakawa, Patrick Morris +1

Given an -vertex pseudorandom graph and an -vertex graph with maximum degree at most two, we wish to find a copy of in , i.e.\ an embedding $φ\colon V(H)\to V(…

math.CO2019★ 22 cited

Ramsey properties of randomly perturbed graphs: cliques and cycles

Shagnik Das, Andrew Treglown

Given graphs , a graph is -Ramsey if for every colouring of the edges of with red and blue, there is a red copy of or a blue copy of . In thi…