5 citations · 20 across the 14 of their papers we have counts for
11 papers · 1 filter
Lean-verified lower bounds for the Shannon capacity of odd cycles
Pjotr Buys, Sven Polak, Jeroen Zuiddam
We give new lower bounds for the Shannon capacities of small odd cycles: , , ,…
Density of reliability roots of simple graphs in the unit disk
Pjotr Buys
Brown and Colbourn (1992) showed that the complex roots of the reliability polynomial of connected multigraphs are dense in the unit disk and that the closure of the real roots is…
A group-theoretic approach to Shannon capacity of graphs and a limit theorem from lattice packings
Pjotr Buys, Sven Polak, Jeroen Zuiddam
We develop a group-theoretic approach to the Shannon capacity problem. Using this approach we extend and recover, in a structured and unified manner, various families of previously…
Triangle-free graphs with the fewest independent sets
Pjotr Buys, Jan van den Heuvel, Ross J. Kang
Given and a positive integer , let be a triangle-free graph on vertices with average degree . With an elegant induction, Shearer (1983) tightened a seminal resu…
Reconfiguration of Independent Transversals
Pjotr Buys, Ross J. Kang, Kenta Ozeki
Given integers and , suppose there is a graph of maximum degree and a partition of its vertices into blocks of size at least . By a seminal result of Haxel…
The asymptotic spectrum distance, graph limits, and the Shannon capacity
David de Boer, Pjotr Buys, Jeroen Zuiddam
Determining the Shannon capacity of graphs is a long-standing open problem in information theory, graph theory and combinatorial optimization. Over decades, a wide range of upper a…
On boundedness of zeros of the independence polynomial of tori
David de Boer, Pjotr Buys, Han Peters +1
We study boundedness of zeros of the independence polynomial of tori for sequences of tori converging to the integer lattice. We prove that zeros are bounded for sequences of balan…
Optimal zero-free regions for the independence polynomial of bounded degree hypergraphs
Ferenc Bencs, Pjotr Buys
In this paper we investigate the distribution of zeros of the independence polynomial of hypergraphs of maximum degree . For graphs the largest zero-free disk around zero was de…
The limit of the zero locus of the independence polynomial for bounded degree graphs
Ferenc Bencs, Pjotr Buys, Han Peters
The goal of this paper is to accurately describe the maximal zero-free region of the independence polynomial for graphs of bounded degree, for large degree bounds. In previous work…
Zeros, chaotic ratios and the computational complexity of approximating the independence polynomial
David de Boer, Pjotr Buys, Lorenzo Guerini +2
The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the polynomial is related to ph…
On the location of roots of the independence polynomial of bounded degree graphs
Pjotr Buys
In [1] Peters and Regts confirmed a conjecture by Sokal by showing that for every there exists a complex neighborhood of the interval $\left[0, \frac{\le…