We propose three new conjectures on perfect matchings in cubic graphs. The weakest conjecture is implied by a well-known conjecture of Berge and Fulkerson. The other two conjectures are a strengthening of the first one. All conjectures are trivially verified for 3-edge-colorable cubic graphs and by computer for all snarks of order at most 34
New conjectures on perfect matchings in cubic graphs / Mazzuoccolo, G.. - In: ELECTRONIC NOTES IN DISCRETE MATHEMATICS. - ISSN 1571-0653. - 40:(2013), pp. 235-238. (Combinatorics 2012 Perugia Giugno 2012) [10.1016/j.endm.2013.05.042].
New conjectures on perfect matchings in cubic graphs
Mazzuoccolo, Giuseppe
2013
Abstract
We propose three new conjectures on perfect matchings in cubic graphs. The weakest conjecture is implied by a well-known conjecture of Berge and Fulkerson. The other two conjectures are a strengthening of the first one. All conjectures are trivially verified for 3-edge-colorable cubic graphs and by computer for all snarks of order at most 34
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