8 citations · 9 across the 10 of their papers we have counts for
12 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…
On odd covers of cliques and disjoint unions
Calum Buchanan, Alexander Clifton, Eric Culver +5
Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order…
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…
Tropical Geometry of Rado Matroids
Calum Buchanan, Richard Danner
In this note, we characterize the products of simplicial generators for the Chow ring of a loopless matroid, extending a result of Backman, Eur, and Simpson. We prove that the stab…
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…
Path Odd-Covers of Graphs
Steffen Borgwardt, Calum Buchanan, Eric Culver +3
We introduce and study "path odd-covers", a weakening of Gallai's path decomposition problem and a strengthening of the linear arboricity problem. The "path odd-cover number" $p_2(…
On the Last New Vertex Visited by a Random Walk in a Directed Graph
Calum Buchanan, Paul Horn, Puck Rombach
Consider a simple graph in which a random walk begins at a given vertex. It moves at each step with equal probability to any neighbor of its current vertex, and ends when it has vi…
Toughness of recursively partitionable graphs
Calum Buchanan, Brandon Du Preez, K. E. Perry +1
A simple graph on vertices is said to be recursively partitionable (RP) if , or if is connected and satisfies the following recursive property: for…
Odd Covers of Graphs
Calum Buchanan, Alexander Clifton, Eric Culver +4
Given a finite simple graph , an odd cover of is a collection of complete bipartite graphs, or bicliques, in which each edge of appears in an odd number of bicliques and…
Subgraph complementation and minimum rank
Calum Buchanan, Christopher Purcell, Puck Rombach
Any finite simple graph can be represented by a collection of subsets of such that if and only if and appear together in an odd numb…