Tomáš Kaiser ; Riste Škrekovski - Cycles intersecting edge-cuts of prescribed sizes

dmtcs:3465 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3465
Cycles intersecting edge-cuts of prescribed sizesArticle

Authors: Tomáš Kaiser ORCID1,2; Riste Škrekovski ORCID2,1

  • 1 Institute for Theoretical Computer Science
  • 2 Department of Mathematics

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.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: graph,cycle,edge-cut,covering cycle,coverable set,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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