On Perfect Matching Coverings and Even Subgraph Coverings. Issue 1 (4th March 2015)

• Record Type: Journal Article
• Authors: Hou, Xinmin; Lai, Hong‐Jian; Zhang, Cun‐Quan
• Is Part Of: Journal of graph theory. Volume 81:Issue 1(2016)
• Page Start: 83
• Page End: 91
• Publication Date: 2015-03-04
• Subjects: matching cover -- cycle cover; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21863
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: 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. Häggkvist, K. Markström, 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 a Berge covering. We also obtain some results concerning the so‐called 5‐even subgraph double cover conjecture.