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math.CO2025
The Cycle Counts of Graphs
Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori +1
We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptio…
math.CO2025
Loose elements in binary and ternary matroids
Jagdeep Singh, Thomas Zaslavsky
We call a matroid element "loose" if it is contained in no circuits of size less than the rank of the matroid. A matroid in which all elements are loose is a paving matroid. Acketa…