Geodesic
Nowhere-zero \(k\)-flows of supergraphs
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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Let $G$ be a 2-edge-connected graph with $o$ vertices of odd degree. It is well-known that one should (and can) add $o \over 2$ edges to $G$ in order to obtain a graph which admits a nowhere-zero 2-flow. We prove that one can add to $G$ a set of $\le \lfloor{o \over 4}\rfloor$, $\lceil{1 \over 2}\lfloor{o \over 5}\rfloor\rceil$, and $\lceil{1 \over 2}\lfloor{o \over 7}\rfloor\rceil$ edges such that the resulting graph admits a nowhere-zero 3-flow, 4-flow, and 5-flow, respectively.
DOI : 10.37236/1564
Classification : 05C15, 05C99
Mots-clés : nowhere-zero \(k\)-flow, bridgeless graph, colouring, supergraph, edge deletion problem 
@article{10_37236_1564,
     author = {Bojan Mohar and Riste \v{S}krekovski},
     title = {Nowhere-zero \(k\)-flows of supergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1564},
     zbl = {0984.05031},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1564/}
}
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Bojan Mohar; Riste Škrekovski. Nowhere-zero \(k\)-flows of supergraphs. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1564

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