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math.CO2026
Basis Number of Graphs Excluding Minors
Colin Geniet, Ugo Giocanti
The basis number of a graph is the minimum such that the cycle space of is generated by a family of cycles using each edge at most times. A classical result of Mac…
math.CO2026
A coarse Gallai theorem
Marc Distel, Ugo Giocanti, Jędrzej Hodor +2
We prove that there exist functions and such that for all positive integers and , for every graph and every subset of the vertices of , either contain…