Semi-duality and the cycle double cover conjecture
type: Item
instance of: scholarly article
title: Semi-duality and the cycle double cover conjecture
zbMATH Open document ID: 0607.05019
DOI: 10.1016/0095-8956(86)90054-7
author: Michael Tarsi
published in: Journal of Combinatorial Theory. Series B
publication date: 1986-01-01T00:00:00Z
review text: In what follows, all matroids are binary. A cycle is a disjoint union of circuits. Two matroids are called semi-dual if every cocycle of one of them is a cycle of the other. A cycle double cover (CDC) of a matroid is a family of not necessarily distinct cycles, containing every element of the underlying set exactly twice. The CDC-conjecture (that every bridgeless graph has a CDC) is shown to be equivalent to the statement: Every bridgeless regular matroid has a loopless graphic semi-dual. As an application, the author shows that every bridgeless multigraph containing a Hamiltonian path has a CDC consisting of at most 6 Eulerian subgraphs.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 3981186
zbMATH Keywords: binary matroids
zbMATH Keywords: cycle double cover
zbMATH Keywords: CDC
zbMATH Keywords: bridgeless graph
zbMATH Keywords: bridgeless regular matroid
zbMATH Keywords: Hamiltonian path
reviewed by: András Recski
MaRDI profile type: Publication
full work available at URL: 0095-8956(86)90054-7
OpenAlex ID: W2083487412
cites work: Q5668821
cites work: Shortest coverings of graphs with cycles
cites work: Flows and generalized coloring theorems in graphs
cites work: Q3710541
cites work: Short cycle covers and the cycle double cover conjecture
cites work: Q3916595
cites work: Decomposition of regular matroids
cites work: Nowhere zero flow and circuit covering in regular matroids
cites work: Q4111952
description: scientific article; zbMATH DE number 3981186