P. Danziger

activity

20152022

most citedZero-sum flows for Steiner triple systems

1 citations · 1 across the 2 of their papers we have counts for

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5 papers · 1 filter

math.CO2022

Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem

A. C. Burgess, P. Danziger, A. Pastine +1

In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group $G$ . When $G$ is cyclic, these types of matrices have been widely used to build uniform…

math.CO2018

The Hamilton-Waterloo Problem with even cycle lengths

A. C. Burgess, P. Danziger, T. Traetta

The Hamilton-Waterloo Problem HWP $(v; m, n; α, β)$ asks for a 2-factorization of the complete graph $K_{v}$ or $K_{v} - I$ , the complete graph with the edges of a 1-factor removed, into $α$ …

math.CO2018

On the Hamilton-Waterloo Problem with cycle lengths of distinct parities

Andrea Burgess, Peter Danziger, Tommaso Traetta

Let $K_{v}^{*}$ denote the complete graph $K_{v}$ if $v$ is odd and $K_{v} - I$ , the complete graph with the edges of a 1-factor removed, if $v$ is even. Given non-negative integers $v, M, N…

math.CO2017

Orthogonally Resolvable Matching Designs

Peter Danziger, Sophia Park

An Orthogonally resolvable Matching Design OMD $(n, k)$ is a partition of the edges the complete graph $K_{n}$ into matchings of size $k$ , called blocks, such that the blocks can be r…

math.CO2015★ 1 cited

Zero-sum flows for Steiner triple systems

S. Akbari, A. C. Burgess, P. Danziger +1

Given a $2$ - $(v, k, λ)$ design, $S = (X, B)$ , a {\it zero-sum $n$ -flow} of $S$ is a map $f : B ⟶ {\pm 1, \dots, \pm (n - 1)}$ such that for any poi…