10 citations · 34 across the 20 of their papers we have counts for
7 papers · 1 filter
An Incidence Result for Well-Spaced Atoms in all Dimensions
Peter Bradshaw
We prove an incidence result counting the -rich -tubes induced by a well-spaced set of -atoms. Our result coincides with the bound that would be heuristically predicted by…
Graph colorings with restricted bicolored subgraphs: II. The graph coloring game
Peter Bradshaw
We consider the graph coloring game, a game in which two players take turns properly coloring the vertices of a graph, with one player attempting to complete a proper coloring, and…
Graph colorings with restricted bicolored subgraphs: I. Acyclic, star, and treewidth colorings
Peter Bradshaw
We show that for any fixed integer , a graph of maximum degree has a coloring with colors in which every connected bicolored subgraph contains at mos…
A note on the connected game coloring number
Peter Bradshaw
We consider the \emph{connected game coloring number} of a graph, introduced by Charpentier et al. as a game theoretic graph parameter that measures the degeneracy of a graph with…
Flexible List Colorings in Graphs with Special Degeneracy Conditions
Peter Bradshaw, Tomáš Masařík, Ladislav Stacho
For a given , we say that a graph is -flexibly -choosable if the following holds: for any assignment of color lists of size on ,…
On the cop number of graphs of high girth
Peter Bradshaw, Seyyed Aliasghar Hosseini, Bojan Mohar +1
We establish a lower bound for the cop number of graphs of high girth in terms of the minimum degree, and more generally, in terms of a certain growth condition. We show, in partic…