The weak 3-flow conjecture and the weak circular flow

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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We show that, for each natural number k>1, every graph (possibly with multiple edges but with no loops) of edge-connectivity at least 2k2+k has an orientation with any prescribed outdegrees modulo k provided the prescribed outdegrees satisfy the obvious necessary conditions. For k=3 the edge-connectivity 8 suffices. This implies the weak 3-flow conjecture proposed in 1988 by Jaeger (a natural weakening of Tutteʼs 3-flow conjecture which is still open) and also a weakened version of the more general circular flow conjecture proposed by Jaeger in 1982. It also implies the tree-decomposition conjecture proposed in 2006 by Bárat and Thomassen when restricted to stars. Finally, it is the currently strongest partial result on the (2+ϵ)-flow conjecture by Goddyn and Seymour.
Original languageEnglish
JournalJournal of Combinatorial Theory. Series B
Publication date2012
Volume102
Issue2
Pages521-529
ISSN0095-8956
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 10

Keywords

  • Orientations modulo k, Star decomposition, 3-Flow conjecture
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