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On minimum flow number of graphs. (English) Zbl 0990.05072

The author calls the minimum integer \(\lambda\) for which a graph \(G\) has a nowhere-zero \(\lambda\)-flow the flow number \(\Lambda(G)\) of \(G\). Using explicit constructions he determines \(\Lambda(G)\) for the complete graphs \(K_n\), the complete bipartite graphs \(K_{n,m}\) and the biwheels \(B_n=C_{n-2}+K_2\) as \(\Lambda(K_n)=2\) if \(n\geq 3\) is odd, \(\Lambda(K_n)=3\) if \(n\geq 6\) is even, \(\Lambda(K_{n,m})=2\) if \(n\) and \(m\) are both even, \(\Lambda(K_{n,m})=3\) if \(n\) and \(m\) are not both even, \(\Lambda(B_n)=2\) if \(n\geq 5\) is odd and \(\Lambda(B_n)=2\) if \(n\geq 6\) is even.

MSC:

05C35 Extremal problems in graph theory
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