Semi-duality and the cycle double cover conjecture

Michael Tarsi

doi:10.1016/0095-8956(86)90054-7

Semi-duality and the cycle double cover conjecture

Michael Tarsi^*

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

Define two binary matroids on the same element set to be mutually semi-dual if every cocycle of one of them is a cycle of the other. We observe that the cycle double cover (CDC) conjecture is equivalent to the following statement: Every bridgeless regular matroid has a loopless graphic semi-dual. This observation is used to construct CDCs for some families of graphs. The main result: Every bridgeless multigraph which contains a Hamiltonian path has a CDC consisting of at most 6 Eulerian subgraphs.

Original language	English
Pages (from-to)	332-340
Number of pages	9
Journal	Journal of Combinatorial Theory. Series B
Volume	41
Issue number	3
DOIs	https://doi.org/10.1016/0095-8956(86)90054-7
State	Published - Dec 1986

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10.1016/0095-8956(86)90054-7

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title = "Semi-duality and the cycle double cover conjecture",

abstract = "Define two binary matroids on the same element set to be mutually semi-dual if every cocycle of one of them is a cycle of the other. We observe that the cycle double cover (CDC) conjecture is equivalent to the following statement: Every bridgeless regular matroid has a loopless graphic semi-dual. This observation is used to construct CDCs for some families of graphs. The main result: Every bridgeless multigraph which contains a Hamiltonian path has a CDC consisting of at most 6 Eulerian subgraphs.",

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AB - Define two binary matroids on the same element set to be mutually semi-dual if every cocycle of one of them is a cycle of the other. We observe that the cycle double cover (CDC) conjecture is equivalent to the following statement: Every bridgeless regular matroid has a loopless graphic semi-dual. This observation is used to construct CDCs for some families of graphs. The main result: Every bridgeless multigraph which contains a Hamiltonian path has a CDC consisting of at most 6 Eulerian subgraphs.

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Semi-duality and the cycle double cover conjecture

Abstract

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