Skip to Main content Skip to Navigation
Conference papers

Cycles intersecting edge-cuts of prescribed sizes

Abstract : We prove that every cubic bridgeless graph $G$ contains a $2$-factor which intersects all (minimal) edge-cuts of size $3$ or $4$. This generalizes an earlier result of the authors, namely that such a $2$-factor exists provided that $G$ is planar. As a further extension, we show that every graph contains a cycle (a union of edge-disjoint circuits) that intersects all edge-cuts of size $3$ or $4$. Motivated by this result, we introduce the concept of a coverable set of integers and discuss a number of questions, some of which are related to classical problems of graph theory such as Tutte's $4$-flow conjecture or the Dominating circuit conjecture.
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam <>
Submitted on : Friday, August 14, 2015 - 2:59:45 PM
Last modification on : Thursday, May 11, 2017 - 1:02:52 AM
Long-term archiving on: : Sunday, November 15, 2015 - 11:15:02 AM


Publisher files allowed on an open archive


  • HAL Id : hal-01184454, version 1



Tomáš Kaiser, Riste Škrekovski. Cycles intersecting edge-cuts of prescribed sizes. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.303-308. ⟨hal-01184454⟩



Record views


Files downloads