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Let mt∗ be the largest rational number such that every bridgeless cubic graph G associated with a positive weight ω has t perfect matchings {M1,…,Mt} with ω(∪i=1tMi)≥mt∗ω(G). It is conjectured in this paper that m3∗=45, m4∗=1415, and m5∗=1, which are called the weighted PM-covering conjectures. The counterparts of this new invariant mt∗ and conjectures for unweighted cubic graphs were introduced by...
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