2 citations · 6 across the 9 of their papers we have counts for
10 papers · 1 filter
A refinement on the structure of vertex-critical (, gem)-free graphs
Ben Cameron, Chính T. Hoàng
We give a new, stronger proof that there are only finitely many -vertex-critical (,~gem)-free graphs for all . Our proof further refines the structure of these graphs an…
A Hamilton Cycle in the -Sided Pancake Network
Ben Cameron, Joe Sawada, Aaron Williams
We present a Hamilton cycle in the -sided pancake network and four combinatorial algorithms to traverse the cycle. The network's vertices are coloured permutations $π= p_1p_2\cd…
The node cop-win reliability of unicyclic and bicyclic graphs
Maimoonah Ahmed, Ben Cameron
Various models to quantify the reliability of a network have been studied where certain components of the graph may fail at random and the probability that the remaining graph is c…
Dichotomizing -vertex-critical -free graphs for of order four
Ben Cameron, Chính T. Hoàng, Joe Sawada
For , we prove (i) there is a finite number of -vertex-critical -free graphs and (ii) -vertex-critical -free graphs have at most v…
A note on purely imaginary independence roots
Ben Cameron, Jason I. Brown
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each cardinality and its roots are called independence roots. We investiga…
On the Mean Subtree Order of Graphs Under Edge Addition
Ben Cameron, Lucas Mol
For a graph , the mean subtree order of is the average order of a subtree of . In this note, we provide counterexamples to a recent conjecture of Chin, Gordon, MacPhee, a…