4 papers · 1 filter
Random independent sets and local sparsity
Ewan Davies
We analyze random constructions of independent sets in locally sparse graphs, specifically graphs with bounded maximum average degree in neighborhoods or with fractionally -colo…
Degree-sequence bounds for independent sets via multivariate local occupancy
Ewan Davies, Juspreet Singh Sandhu, Jaehyeon Seo +1
We present new degree-sequence lower bounds on the expected size of an independent set from the hard-core model. For arbitrary graphs, we establish a multivariate lower bound inspi…
On expectations and variances in the hard-core model on bounded degree graphs
Ewan Davies, Juspreet Singh Sandhu, Brian Tan
We extend the study of the occupancy fraction of the hard-core model in two novel directions. One direction gives a tight lower bound in terms of individual vertex degrees, extendi…
On the occupancy fraction of the antiferromagnetic Ising model
Ewan Davies, Olivia LeBlanc
We study the maximum and minimum occupancy fraction of the antiferromagnetic Ising model in regular graphs. The minimizing problem is known to determine a computational threshold i…