Geodesic
Perfect matching covers of cubic graphs of oddness 2
Wuyang Sun1 ; Fan Wang2
1Shandong University (Weihai)
2Nanchang University
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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A perfect matching cover of a graph $G$ is a set of perfect matchings of $G$ such that each edge of $G$ is contained in at least one member of it. Berge conjectured that every bridgeless cubic graph has a perfect matching cover of order at most 5. The Berge Conjecture is largely open and it is even unknown whether a constant integer $c$ does exist such that every bridgeless cubic graph has a perfect matching cover of order at most $c$. In this paper, we show that a bridgeless cubic graph $G$ has a perfect matching cover of order at most 11 if $G$ has a 2-factor in which the number of odd circuits is 2.
DOI : 10.37236/7175
Classification : 05C70

Wuyang Sun  1   ; Fan Wang  2

1 Shandong University (Weihai)
2 Nanchang University 
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     author = {Wuyang Sun and Fan Wang},
     title = {Perfect matching covers of cubic graphs of oddness 2},
     journal = {The electronic journal of combinatorics},
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Wuyang Sun; Fan Wang. Perfect matching covers of cubic graphs of oddness 2. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7175

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