7 papers · 1 filter
Genus Polynomials of Cubic Graphs with Non-Real Roots
MacKenzie Carr, Varpreet Dhaliwal, Bojan Mohar
Given a graph , its genus polynomial is , where is the number of 2-cell embeddings of in an orientable surface of genus . The…
Eternal domination in Cayley graphs
MacKenzie Carr, Nancy E. Clarke, Gary MacGillivray +1
Eternal domination is a process in which a set of guards occupying a dominating set on a graph protects against an infinite sequence of attacks. After a vertex is attacked, one gua…
Cooling graph products
Anthony Bonato, MacKenzie Carr, Caleb Jones +2
The cooling number measures the speed at which a slow-moving influence or contagion spreads on a graph. In this paper, we investigate the cooling number of four classical graph pro…
2-cell embeddings of cubic graphs I. The unstable dual
MacKenzie Carr, Bojan Mohar
In this paper, the first of a two-part series, we explore 2-cell embeddings of cubic graphs, particularly those with small genus. Using local rotations, we introduce a new way of d…
Reconstruction of C_4-free graphs from the set of closed neighborhoods and digital convexity
Steffen Borgwardt, MacKenzie Carr, Ce Chen +4
Fomin, KratochvÃl, Lokshtanov, Mancini, and Telle showed that every -free graph is reconstructible from the \emph{multiset} of closed neighborhoods. We strengthen their res…
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…