78 citations · 83 across the 7 of their papers we have counts for
8 papers · 1 filter
Counting Small Cycle Double Covers
Jorik Jooken, Ben Seamone, Carol T. Zamfirescu
A theorem due to Seyffarth states that every planar -connected -vertex graph has a cycle double cover (CDC) containing at most cycles (a "small" CDC). We extend this th…
Few hamiltonian cycles in graphs with one or two vertex degrees
Jan Goedgebeur, Jorik Jooken, On-Hei Solomon Lo +2
We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as well as correct…
The Speed and Threshold of the Biased Hamilton Cycle Game
Noah Brustle, Sarah Clusiau, Vishnu V. Narayan +3
We show that there is a constant C such that for any , Maker wins the Maker-Breaker Hamilton cycle game in $n+\frac{Cn}{\sqrt{\ln{n}}}…
The Speed and Threshold of the Biased Perfect Matching Game
Noah Brustle, Sarah Clusiau, Vishnu V. Narayan +3
We show that Maker wins the Maker-Breaker perfect matching game in turns when the bias is at least , for any …
A study of cops and robbers in oriented graphs
Devvrit Khatri, Natasha Komarov, Aaron Krim-Yee +4
We consider the well-studied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date. We examine the relationship between…
Fully Active Cops and Robbers
Ilya Gromovikov, William B. Kinnersley, Ben Seamone
We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum…