10.9k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
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8 papers · 2 filters
Bootstrap percolation in Ore-type graphs
Alexandra Wesolek
The -neighbour bootstrap process describes an infection process on a graph, where we start with a set of initially infected vertices and an uninfected vertex becomes infected as…
Cops and robbers on directed and undirected abelian Cayley graphs
Peter Bradshaw, Seyyed Aliasghar Hosseini, Jérémie Turcotte
We show that the cop number of directed and undirected Cayley graphs on abelian groups has an upper bound of the form of , where is the number of vertices, by intr…
Flows on flow-admissible signed graphs
Matt DeVos, Jiaao Li, You Lu +3
In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero -flow. Bouchet himself proved that such signed graphs admit nowhere-zero $21…
The sandpile group of a polygon flower
Haiyan Chen, Bojan Mohar
Let be a cycle of length , and let be polygon chains. A polygon flower is a graph obtained by identifying the th edge of…
Vertex arboricity of cographs
Sebastián González Hermosillo de la Maza, Pavol Hell, César Hernández Cruz +2
Arboricity is a graph parameter akin to chromatic number, in that it seeks to partition the vertices into the smallest number of sparse subgraphs. Where for the chromatic number we…
Kochen-Specker sets in four-dimensional spaces
Brandon Elford, Petr Lisonek
For the first time we construct an infinite family of Kochen-Specker sets in a space of fixed dimension, namely in R^4. While most of the previous constructions of Kochen-Specker s…
A tree distinguishing polynomial
Pengyu Liu
We define a bivariate polynomial for unlabeled rooted trees and show that the polynomial of an unlabeled rooted tree is the generating function of a class of subtrees of . W…
Branch-depth: Generalizing tree-depth of graphs
Matt DeVos, O-joung Kwon, Sang-il Oum
We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns clos…