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2016

On Perfect Matching Coverings and Even Subgraph Coverings

3 years 3 months ago
On Perfect Matching Coverings and Even Subgraph Coverings
: A perfect matching covering of a graph G is a set of perfect matchings of G such that every edge of G is contained in at least one member of it. Berge conjectured that every bridgeless cubic graph admits a perfect matching covering of order at most 5 (we call such a collection of perfect matchings a Berge covering of G). A cubic graph G is called a Kotzig graph if G has a 3-edge-coloring such that each pair of colors forms a hamiltonian circuit (introduced by R. H¨aggkvist, K. Markstr¨om, J Combin Theory Ser B 96 (2006), 183–206). In this article, we prove that if there is a vertex w of a cubic graph G such that G − w, the graph obtained from G − w by suppressing all degree two vertices is a Kotzig graph, then G has Contract grant sponsor: CNNSF; Contract grant number: 11271348; Contract grant sponsor: NSA; Contract grant numbers: H98230-12-1-0233 and H98230-14-1-0154; Contract grant sponsor: NSF; Contract grant number: DMS-1264800. Journal of Graph Theory C 2015 Wiley Period...
Xinmin Hou, Hong-Jian Lai, Cun-Quan Zhang
Added 06 Apr 2016
Updated 06 Apr 2016
Type Journal
Year 2016
Where JGT
Authors Xinmin Hou, Hong-Jian Lai, Cun-Quan Zhang
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