2 citations · 4 across the 7 of their papers we have counts for
8 papers · 1 filter
On Deeply Critical Oriented Cliques
Christopher Duffy, Pavan P D, Sandeep R. B. +1
In this work we consider arc criticality in colourings of oriented graphs. We study deeply critical oriented graphs, those graphs for which the removal of any arc results in a decr…
A Note on Colourings of Connected -edge Coloured Cubic Graphs
Christopher Duffy
In this short note we show that every connected -edge coloured cubic graph admits an -colouring. This lowers the best known upper bound for the chromatic number of connected…
A Note on Colourings of Connected Oriented Cubic Graphs
Christopher Duffy
In this note we show every orientation of a connected cubic graph admits an oriented 8-colouring. This lowers the best-known upper bound for the chromatic number of the family of o…
Oriented Colourings of Graphs with Maximum Degree Three and Four
Christopher Duffy, Gary MacGillivray, Eric Sopena
We show that any orientation of a graph with maximum degree three has an oriented 9-colouring, and that any orientation of a graph with maximum degree four has an oriented 69-colou…
The Spread of Voting Attitudes in Social Networks
Jordan Barrett, Christopher Duffy, Richard Nowakowski
The Shapley-Shubik power index is a measure of each voters power in the passage or failure of a vote. We extend this measure to graphs and consider a discrete-time process in which…
Chromatic Polynomials of Oriented Graphs
Danielle Cox, Christopher Duffy
The oriented chromatic polynomial of a oriented graph outputs the number of oriented -colourings for any input . We fully classify those oriented graphs for which the oriente…