Cycle and cocycle coverings of graphs
Sean R. McGuinness · Journal of Graph Theory · 2010
Abstract In this article, we show that for any simple, bridgeless graph G on n vertices, there is a family 𝒞 of at most n−1 cycles which cover the edges of G at least twice. A similar, dual result is also proven for cocycles namely: for any loopless graph G on n vertices and ε edges having cogirth g*⩾3 and k(G) components, there is a family of at most ε−n+k(G) cocycles which cover the edges of G at least twice. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 270–284, 2010