2025/09/05 by Máčajová, Edita, Mazák, Ján
#05C70 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.05501
For a bridgeless cubic graph G, m3(G) is the ratio of the maximum number of edges of G covered by the union of 3 perfect matchings to |E(G)|. We prove that for any r∈ [4/5, 1), there exist infinitely many cubic graphs G such that m3(G) = r. For any r∈ [9/10, 1), there exist infinitely many cyclically 4-connected cubic graphs G with m3(G) = r.