منابع مشابه
Realizing Degree Sequences with Graphs Having Nowhere-Zero 3-Flows
The following open problem was proposed by Archdeacon: Characterize all graphical sequences π such that some realization of π admits a nowhere-zero 3-flow. This open problem is solved in this paper with the following complete characterization: A graphical sequence π = (d1, d2, . . . , dn) with minimum degree at least two has a realization that admits a nowhere-zero 3-flow if and only if π 6= (3...
متن کاملNowhere-Zero 3-Flows in Signed Graphs
Tutte observed that every nowhere-zero k-flow on a plane graph gives rise to a kvertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph G has a face-k-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero k-flow. However, if the surface is nonorientable, then a...
متن کاملNowhere-zero 5-flows
We prove that every cyclically 6-edge-connected cubic graph with oddness at most 4 has a nowhere-zero 5-flow. Therefore, a possible minimum counterexample to the 5-flow conjecture has oddness at least 6.
متن کاملNowhere-zero 3-flows and modulo k-orientations
Article history: Received 30 October 2011 Available online 20 August 2013
متن کاملTitle Nowhere - Zero 3 - Flows in Signed Graphs
Tutte observed that every nowhere-zero k-flow on a plane graph gives rise to a kvertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph G has a face-k-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero k-flow. However, if the surface is nonorientable, then a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.11.045