5 papers
On Cycles in Multiset Permutations, Parking Functions, and Related Structures
Calum Buchanan, Fabian Burghart, Stephan Wagner +1
In this paper we study cycles in multiset permutations and parking functions. As combinatorial objects, multiset permutations are essential building blocks for mappings and permuta…
On fixing and distinguishing numbers of trees
Calum Buchanan, Peter Dankelmann, Isabel Harris +3
A graph is -distinguishable if there is a labeling of its vertices with labels such that the only automorphism of which preserves the labeling is the identity. The d…
Vertex addition to a ball graph with application to reliability and area coverage in autonomous swarms
Calum Buchanan, Puck Rombach, James Bagrow +1
A unit ball graph consists of a set of vertices, labeled by points in Euclidean space, and edges joining all pairs of points within distance 1. These geometric graphs are used to m…
Trail Trap: a variant of Partizan Edge Geography
Calum Buchanan, MacKenzie Carr, Alexander Clifton +4
We study a two-player game played on undirected graphs called {\sc Trail Trap}, which is a variant of a game known as {\sc Partizan Edge Geography}. One player starts by choosing a…
A lower bound on the saturation number and a strengthening for triangle-free graphs
Calum Buchanan, Puck Rombach
The saturation number of a graph and positive integer is the minimum size of a graph of order which does not contain a subgraph isomorphic to…