9 papers · 1 filter
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…
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…