It is proved that if G is a connected cubic graph of order p all of whose bridges lie on r edge-disjoint paths of G, then every maximum matching of G contains at least P/2 − └2r/3┘ edges. Moreover, this result is shown to be best possible. © 1987, Australian Mathematical Society. All rights reserved.
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Chartrand, G., Kapoor, S. F., Oellermann, O. R., & Ruiz, S. (1987). On maximum matchings in cubic graphs with a bounded number of bridge-covering paths. Bulletin of the Australian Mathematical Society, 36(3), 441–447. https://doi.org/10.1017/S0004972700003737