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- W2912763084 abstract "In connection to the 5-flow conjecture, a modulo 5-orientation of a graph G is an orientation of G such that the indegree is congruent to outdegree modulo 5 at each vertex. Jaeger conjectured that every 9-edge-connected multigraph admits a modulo 5-orientation, whose truth would imply Tutte’s 5-flow conjecture. In this paper, we study the problem of modulo 5-orientation for given multigraphic degree sequences. We prove that a multigraphic degree sequence d=(d1,…,dn) has a realization G with a modulo 5-orientation if and only if di≠1,3 for each i. In addition, we show that every multigraphic sequence d=(d1,…,dn) with min1≤i≤ndi≥9 has a 9-edge-connected realization which admits a modulo 5-orientation for every possible boundary function. This supports the above mentioned conjecture of Jaeger." @default.
- W2912763084 created "2019-02-21" @default.
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- W2912763084 date "2019-05-01" @default.
- W2912763084 modified "2023-10-14" @default.
- W2912763084 title "Modulo 5-orientations and degree sequences" @default.
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- W2912763084 doi "https://doi.org/10.1016/j.dam.2019.01.021" @default.
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