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math.CO2025
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…
math.CO2025
On a conjecture of Faudree and Schelp
Jan Goedgebeur, Jorik Jooken, Michiel Provoost +1
In 1976 Faudree and Schelp conjectured that in a hamiltonian-connected graph on vertices, any two distinct vertices are connected by a path of length for every .…
math.CO2025
Network fault costs based on minimum leaf spanning trees
Jan Goedgebeur, Jarne Renders, Gábor Wiener +1
We study the fault-tolerance of networks from both the structural and computational point of view using the minimum leaf number of the corresponding graph , i.e. the minimum num…